A square prism has sides of length 3 \text{ cm}, 3 \text{ cm} and 14 \text{ cm} as shown in the diagram:
If the diagonal HF has a length of z \text{ cm}, find the value of z to two decimal places.
If the size of \angle DFH is \theta \degree, find \theta to two decimal places.
All edges of the given cube are 7 \text{ cm} long:
Find the exact length of the following:
EG
AG
Find the following angles to the nearest degree:
\angle EGH
\angle EGA
\angle AHG
\angle AGH
A rectangular prism has dimensions as shown:
Find the following lengths in surd form:
Find the area of \triangle ADG, in surd form.
Find the size of \angle DAG, correct to two decimal places.
A trianglular wedge has been inserted into the box as shown:
Find the size of angle x, correct to two decimal places.
A different trianglular wedge has been inserted into the box as shown:
Find the size of angle y, correct to two decimal places.
The box have a triangular divider placed inside it, as shown in the diagram:
If z = AC, find the value of z to two decimal places.
Find the area of the divider correct to two decimal places.
Consider the cube as shown:
Find the size of:
\alpha
\beta
\gamma
Calculate the exact length of x.
Calculate the exact length of y.
Hence, find the angle \theta to the nearest degree.
Consider the given rectangular prism:
Find the length x.
Hence, find the length of the prism's diagonal y.
Find the angle \theta to the nearest degree.
A 25 \text{ cm }\times 11 \text{ cm }\times 8 \text{ cm} cardboard box contains an insert (the shaded area) made of foam:
Find the exact length b of the base of the foam insert.
Find the area of foam in the insert, rounded to the nearest square centimetre.
Find the value of \theta to the nearest degree.
The diagram shows a triangular prism:
Find the exact length of AC.
Find the size of \angle ACF in degrees.
Find the exact length of AF.
Find the size of\angle AFC to the nearest degree.
A triangular prism has dimensions as shown in the diagram:
Find the size of \angle AED, correct to two decimal places.
Find the exact length of CE.
Find the exact length of BE.
Find the size of \angle BEC, correct to two decimal places.
Find the exact length of CX.
Find the size of \angle BXC, correct to two decimal places.
The following pyramid has a square base with side length 8 \text{ cm}, and all slanted edges are 12 \text{ cm} in length:
Find the exact length of MD.
Find the size of \angle PDM, correct to two decimal places.
Find the exact height of the pyramid, MP.
Find the length of MN.
Find the exact length of PN.
Find the size of \angle PNM, correct to two decimal places.
Find the size of \angle PDC, correct to two decimal places.
This triangular prism shaped box labelled ABCDEF needs a diagonal support inserted as shown:
Write an expression for the length of BF in terms of BD and DF.
Hence, find the length of AF in terms of AB, BD and DF.
If AB = 19, BD = 30 and DF = 43, find the length of AF to two decimal places.
Find the length of AF be if AB, BD and DF increased by 10. Give your answer to two decimal places.
A room measures 5 \text{ m} in length and 4 \text{ m} in width. The angle of elevation from the bottom left corner to the top right corner of the room is 57 \degree.
Find the exact distance from one corner of the floor to the opposite corner of the floor.
Find the height of the room. Round your answer to two decimal places.
Find the angle of elevation from the bottom corner of the 5 \text{ m} long wall to the opposite top corner of the wall. Round your answer to two decimal places.
Find the angle of depression from the top corner of the 4 \text{ m} long wall to the opposite bottom corner of the wall. Round your answer to two decimal places.
The angle of elevation to the top of a 22 \text{ m} high statue is 54 \degree from a point, A, due west of the statue. The point B is located 60 \text{ m} due south of point A.
Find the distance, x, from point A to the base of the statue, correct to two decimal places.
Hence, find y, the distance from point B to the base of the statue, correct to one decimal place.
Hence, find \theta, the angle of elevation from point B to the top of the statue, correct to the nearest degree.
A cockroach starts at point B and crawls towards point C at 10 \text{ cm/min} on a 3.4 \text{ m} high ceiling. Sally is standing at a point A:
Calculate the distance in centimeters the cockroach will have crawled in the 3 minutes it take to reach point C.
The cockroach is now at point C. Calculate y, the distance in centimetres Sally will be from the point directly below the cockroach. Round your answer to two decimal places.
Calculate \theta, the angle of elevation from Sally to the cockroach at point C.
From a point 15\text{ m} due north of a tower, the angle of elevation of the tower is 32 \degree.
Find the height of the tower h. Round your answer to two decimals places.
Find the size \theta of the angle of elevation of the tower at a point 20\text{ m} due east of the tower. Round your answer to the nearest degree.
A hot air balloon travelling at 950 \text{ m/h} at a constant altitude of 3000 \text{ m} is observed to have an angle of elevation of 76 \degree. After 20 minutes, the angle of elevation is 71 \degree.
Determine the initial horizontal distance x from the observer to the balloon. Round your answer to the nearest metre.
Determine the final horizontal distance y from the observer to the balloon. Round your answer to the nearest metre.
Hence, calculate the angle \theta through which the observer has turned during the 20 minutes. Round your answer to the nearest degree.
A lighthouse is 174\text{ m} above sea level. The angle of elevation of the lighthouse from Boat 1 is 15 \degree. The angle of elevation of the lighthouse from Boat 2 is 19 \degree. The distance between the two boats is 1\text{ km}.
Find the horizontal distance x from Boat 1 to the lighthouse to the nearest metre.
Find the horizontal distance y from Boat 2 to the lighthouse to the nearest metre.
The two boats form an angle of \theta at the base of the lighthouse. Find \theta to the nearest degree.
AC and BD are vertical posts. AC is west of BD. AC = h and BD = 1.5 h. P is on the ground, south of AC.
The angle of elevation of C from P is y \degreeand the angle of elevation of D from P is z \degree. The angle of elevation D from C is x \degree.
Prove the following:\cot ^{2}\left( x \degree\right) + 4 \cot ^{2}\left( y \degree\right) = 9 \cot ^{2}\left( z \degree\right)
Two buildings AB and CD are 200\text{ m} apart. The angle of elevation of the top B of the first building from a point E, on the ground is 22 \degree, and from the point F, also on the ground is 18 \degree. The points E and F are 100\text{ m} apart. EF is parallel to AC. The heights of the buildings AB and CD are 100\text{ m} and 50 \text{ m} respectively.
Find the length of AE to one decimal place.
Find the length of AF to one decimal place.
Find the size of \angle AFE to the nearest degree.
Find the length CF to one decimal place.
Find the size of \angle CFE to one decimal place.
Find the length of CE to one decimal place.
Find the size of the angle of elevation of the top D of the second building from the point F, correct to the nearest degree.
Find the size of the angle of elevation of the top D of the second building from the point E, correct to the the nearest degree.
A person walks 2000 \text{ m} due north along a road from point A to point B. The point A is due east of the mountain OM, where M is the top of the mountain. The point O is directly below point M and is on the same horizontal plane as the road. The height of the mountain above point O is h metres. From point A, the angle of elevation to the top of the mountain is 15 \degree. From point B, the angle of elevation to the top of the mountain is 13 \degree.
Show that if the length of AO is x, then:x \tan 15 \degree = \sqrt{x^{2} + 2000^{2}} \tan 13 \degree
Find the value of x in metres. Round your answer to one decimal place.
Hence or otherwise, calculate the height of the mountain to one decimal place.
A cone has radius 7\text{ cm} and a slant height of 13\text{ cm}:
Find the vertical angle, \theta, at the top of the cone in degrees and minutes.
A pole is seen by two people, Jenny and Matt:
Matt is x\text{ m} from the foot of the pole. Find x to the nearest metre.
Find the height of the pole h to the nearest metre.
Two straight paths to the top of a cliff are inclined at angles of 24 \degree and 21 \degree to the horizontal:
If path A is 115\text{ m} long, find the height h of the cliff, rounded to the nearest metre.
Find the length x of path B, correct to the nearest metre.
Let the paths meet at 46 \degree at the base of the cliff. Find their distance apart, y, at the top of the cliff, to the nearest metre.
Three satellites, A, B, and C, used for GPS navigation are orbiting the earth. The distance between satellites A and B is 8.27\text{ km}. A, B, and C are in the same plane in space, and E is a car on earth. The angle \angle BAE = 45 \degree.
Find the distance x between satellite A and satellite C in kilometres. Round your answer to two decimal places.
Find the distance y between satellites B and C in kilometres. Round your answer to two decimal places.
Find the distance z from satellite A to the car E in kilometres. Round your answer to two decimal places.
Ally and Brad are playing on a merry-go-round. C is the centre of the merry-go-round. Ally is leaning against pole AP which is 0.7\text{ m} tall. Brad is at the point B.
Find the radius r of the merry-go-round in metres, correct to one decimal place.
Find the distance AB between Ally and Brad in metres. Round your answer to one decimal place.
Hence or otherwise, find \angle CAB, correct to the nearest degree.
There are thugs standing at point M and N. The thug at point M is 30\text{ m} away from the base of the tree, and Robin Hood, standing on a branch at point R, is looking down at him with an angle of depression of 38 \degree. The angle of elevation from N to B is 34 \degree.
Find the following, rounding your answers to one decimal place:
The height h of the tree in metres if it reaches 1.5\text{ m} above the branch.
The distance Robin would need to shoot from point R to the man standing at point M.
The distance Robin would need to shoot from point B to the man standing at point N.
The distance between the man at point M and the man at point N.
The height of a lighthouse is 210 \text{ m} above sea level. The angle of elevation to the top of the lighthouse from a boat P is 17 \degree. The bearing of the lighthouse from the boat is \text{N } 44 \degree \text{E}. The angle of elevation to the top of the lighthouse from a second boat Q is 12 \degree. The bearing of the lighthouse from the second boat is \text{N }32 \degree \text{W}.
Find the following to the nearest metre:
The horizontal distance from the lighthouse to P.
The horizontal distance from the lighthouse to Q.
The distance between the two boats.
Find the following to the nearest degree:
The angle made at P between Q and the base of the lighthouse.
The bearing of boat Q from boat P.
Three tourists A, B and C are observing the Eiffel Tower from the ground, A is north of the tower, C is due east of the tower, and B is on the line of sight from A to C. The angles of elevations to the top of the Eiffel Tower from A, B and C are 26 \degree,\ 28 \degreeand 30 \degree, respectively.
Let h be the height of the Eiffel Tower. Find the following to the nearest degree:
The angle \theta at A from the base of the Eiffel Tower to C.
The angle \phi at B from the base of the Eiffel Tower to A.
The bearing of B from the Eiffel Tower.
David walks along a straight road. At one point, he notices a tower on a bearing of 054 \degree with an angle of elevation of 20 \degree. After David walks 220\text{ m}, the tower is on a bearing of 341 \degree with an angle of elevation of 25 \degree.
Find the angle \theta that David has walked with respect to the tower. Round your answer to the nearest degree.
Find the height of the tower to the nearest metre.
From the top of a vertical pole, the angle of depression to Ian standing at the foot of the pole is 43 \degree. Liam is on the other side of the pole such that the pole is directly between him and Ian, and the angle of depression from the top of the pole to Liam is 52 \degree. The boys are standing 58\text{ m} apart.
Find the height of the pole to the nearest metre.
From point A, 94\text{ m} due south of the base of a tower, the angle of elevation is 36 \degree to the top of the tower. Point B is 125\text{ m} due east of the tower.
Find the height of the tower, rounded to the nearest metre.
Find the angle \theta of elevation of the top of the tower from point B. Round your answer to the nearest degree.
A cable car 100\text{ m} above the ground is seen to have an angle of elevation of 64 \degree when it is on a bearing of 348 \degree. After a minute, it has an angle of 68 \degree and is on a bearing of 023 \degree.
Calculate the distance that the cable car travelled during the minute. Round your answer to the nearest metre.
Find the cable car's speed, correct to one decimal place.