Find the value of the pronumeral in the following triangles, correct to two decimal places:
Consider the following diagram:
Calculate the value of a, to the nearest centimetre.
Given the value of \tan \theta, find the value of b in the following diagrams. Round your answers to one decimal place if necessary.
\tan \theta = 0.4
\tan \theta = \dfrac{2}{3}
In the following diagram, Neil's home is located at point A, and Neil is standing at point B.
If d is the distance between Neil and his home, find the value of d correct to two decimal places.
A lighthouse is positioned at point A and a boat is at point B in the given diagram.
Find the length of AB to two decimal places.
Evaluate \sin 69 \degree, correct to two decimal places.
Given \tan x = \dfrac{9}{5}, determine x to the nearest degree.
Find \theta, to the nearest degree, given 0 \degree \leq \theta \leq 90 \degree:
For each of the following triangles, find the value of x to the nearest degree:
Consider \triangle ABC:
Find \cos \theta.
Find \tan \alpha.
For the given triangle \cos \theta = \dfrac{6}{10}.
What angle is represented by \theta?
Find the value of x.
Find the value of \sin \theta.
Find the value of \tan \theta.
For the given triangle \sin \theta = \dfrac{4}{5}.
What angle is represented by \theta?
Find the value of x.
Find the value of \cos \theta.
Find the value of \tan \theta.
Consider the following triangle:
Find \sin \theta.
Find \cos \theta.
Find \dfrac{\sin \theta}{\cos \theta}.
Find \tan \theta.
What do you notice?
An isosceles triangle has equal side lengths of 10 \text{ cm} and a base of 8 \text{ cm} as shown.
Calculate the size of angle A to one decimal place.
Find the value of \tan \theta for the following triangle:
Find the value of the pronumeral(s) in the following diagrams, correct to the nearest whole number:
Find the height of the tree, h, to two decimal places:
The longer side of a rectangular garden measures 14 \text{ m} . A diagonal path makes an angle of 26 \degree with the longer side of the garden.
If the length of the shorter side of the garden is y \text{ m} , calculate y to two decimal places.
If d is the distance between the base of the wall and the base of the ladder, find the value of d to two decimal places.
A ladder is leaning at an angle of 44 \degree against a 1.36 \text{ m} high wall. Find the length of the ladder, to two decimal places.
A ladder measuring 2.36 \text{ m} in length is leaning against a wall.
If the angle the ladder makes with the ground is y \degree, find the value of y to two decimal places.
A girl is flying a kite that is attached to the end of a 23.4 \text{ m} length of string. The angle between the string and the vertical is 21 \degree. The girl is holding the string 2.1 \text{ m} above the ground.
Find x, correct to two decimal places.
Hence, find the height, h, of the kite above the ground, correct to two decimal places.
In the diagram, a string of lights joins the top of the tree to a point on the ground 23.9 \text{ m} away. If the angle that the string of lights makes with the ground is \theta \degree, find \theta to two decimal places.
A ladder measuring 1.65 \text{ m} in length is leaning against a wall. If the angle the ladder makes with the wall is y \degree, find y to two decimal places.
In \triangle MNP, \angle MNP = 90 \degree, MN = 18 and NP = 17. If the size of \angle MPN is t \degree, find t correct to the nearest degree.
Consider the given figure:
Find x, correct to two decimal places.
Find y, correct to two decimal places.
Find z, correct to two decimal places.
Find the value of \tan \theta in the following trapezium:
Consider the following figure:
Find y correct to one decimal place.
Find x + y , correct to one decimal place.
Use these rounded values to find x correct to one decimal place.
Consider the following figure:
Find the size of angle x in degrees, correct to two decimal places.
Find the size of angle y in degrees, correct to two decimal places.
A ship dropped anchor off the coast of a resort. The anchor fell 73 \text{ m} to the sea bed. During the next 5 hours, the ship drifted 182 \text{ m}. Calculate the angle, x, between the anchor line and the surface of the water, rounded to the nearest degree.
The final approach of an aeroplane when landing requires an angle of descent of about 4 \degree.
If the plane is directly above a point 51 \text{ m} from the start of the runway, find d, the height of the plane above the ground to the nearest metre.
The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10\,369 \text{ m} above the ground and is still 23\,444 \text{ m} from the runway.
If \theta \degree is the angle at which the plane should approach, find \theta to one decimal place.
A sand pile has an angle of 40 \degree and is 10.6 \text{ m} wide.
Find the height of the sand pile, h, to one decimal place.
A suspension bridge is being built. The top of the concrete tower is 35.5 \text{ m} above the bridge and the connection point for the main cable is 65.9 \text{ m} from the tower.
Assume that the concrete tower and the bridge are perpendicular to each other.
Find the length of the cable to two decimal places.
Find the angle the cable makes with the road to two decimal places.
An isosceles triangle ABC has been inscribed in a circle of centre O. The heights BD and OD are 13 \text{ cm} and 5 \text{ cm}, respectively.
Find the length of the radius of the circle.
Find the length of DC correct to 2 decimal places.
Calculate the length of the chord AC correct to two decimal places.
A 13.7 \text{ m} long string of lights joins the top of a tree to a point on the ground. If the tree is 3.7 \text{ m} tall, find \theta, the angle the string of lights would make with the tree, rounded to two decimal places.
Georgia is riding her pushbike up a hill that has an incline of 7 \degree. If she rides her bike 689 \text{ m} up the hill, find the horizontal distance from her starting point, to the nearest metre.
Jack is standing at the tip of a tree's shadow and knows that the angle from the ground to the top of the tree is 34 \degree. If Jack is standing 29 \text{ m} away from the base of the tree, find the height of the tree to two decimal places.
Consider the following diagram:
Find y, correct to two decimal places.
Find w, correct to two decimal places.
Hence, find x, correct to one decimal place.
In the following diagram, \angle CAE = 61 \degree, \angle CBE = 73 \degree and CE = 25.
Find the length of AE, correct to four decimal places.
Find the length of BE, correct to four decimal places.
Hence, find the length of AB, correct to two decimal places.
Find the length of BD, correct to one decimal place.
A safety fence is constructed to protect tourists from the danger of an eroding castle toppling down. The surveyor takes an angle measurement to the top of the tower of 10 \degree. She then walks 29 \text{ m} towards the tower and takes another reading of 22 \degree.
Find the value of h to the nearest metre.
