Express the following in degrees correct to two decimal places:
Express the following in degrees, minutes and seconds:
For each of the following right-angled triangles, write down the ratio of the sides represented by:
For each of the following right-angled triangles, evaluate:
Consider the following triangle:
Find \sin \theta.
Find \cos \theta.
Find \dfrac{\sin \theta}{\cos \theta}.
Find \tan \theta.
What do you notice?
Consider the following triangle:
Find the value of \sin \left(90 \degree - \theta\right).
Find the value of \cos \theta.
What do you notice?
Consider the following triangle:
Find the value of \cos \left(90 \degree - \theta\right).
Find the value of \sin \theta.
What do you notice?
For each of the following right-angled triangles, find the value of:
x
\sin \theta
\cos \theta
For each of the following right-angled triangles, find the value of:
The unknown side.
\tan \theta
In the following triangle, \sin \theta = \dfrac{4}{5}:
Which angle is represented by \theta?
Find the value of \cos \theta.
Find the value of \tan \theta.
In the following triangle \tan \theta = \dfrac{15}{8}.
Which angle is represented by \theta?
Find \cos \theta.
Find \sin \theta.
In the following triangle \cos \theta = \dfrac{6}{10}:
Which angle is represented by \theta?
Find \sin \theta.
Find \tan \theta.
Find the value of \tan \theta for the following triangle:
Find the value of the pronumeral in the following triangles, correct to two decimal places:
Determine the length of AC, 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}
Find \theta, to one decimal place, given 0 \degree \leq \theta \leq 90 \degree:
\sin \theta = 0.6125
\tan \theta = 2.748
\cos \theta = 0.1472
Find \theta, to the nearest degree, given 0 \degree \leq \theta \leq 90 \degree:
For each of the following right-angled triangles, find the value of x to the nearest degree:
For each of the following right-angled triangles, find the value of \theta to the nearest minute:
Consider the following diagram:
Find the value of x, correct to two decimal places.
Find the value of x, correct to the nearest minute.
State the exact value of the following:
\sin 60 \degree
\cos 60 \degree
\tan 30 \degree
\sin 45 \degree
Given that \sin \theta = \dfrac{1}{2} in a right triangle:
State the value of \theta.
Hence, find \cos \theta.
Find the exact value of the pronumeral(s) in the following triangles:
Use exact values to solve for \theta in the following triangles:
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 f, correct to two decimal places.
In the given diagram:
AB is a tangent to a circle with centre O.
OB is 24 \text{ cm} long and cuts the circle at C.
Find the radius of the circle, r, correct to one decimal place.
Find the length of BC to the nearest centimetre.
Consider the following diagram:
Find x correct to two decimal places.
Find w correct to one decimal place.
Find z correct to the nearest whole number.
Consider the following figure. Find the value of h correct to the nearest integer.
Find the value of x, the side length of the parallelogram, to the nearest centimetre.
Consider the given figure:
Find the following, rounding your answers to two decimal place:
x
y
z
Consider the following figure:
Find the following, rounding your answers to two decimal place:
x
y
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.
During a particular time of the day, a tree casts a shadow of length 24\text{ m}. The height of the tree is estimated to be 7\text{ m}. Find the angle \theta, formed by the length of the shadow and the arm extending from the edge of the shadow to the height of the tree. Round your answer to two decimal places.
During rare parts of Mercury and Venus' orbit, the angle from the Sun to Mercury to Venus is a right angle, as shown in the diagram:
The distance from Mercury to the Sun is 60\,000\,000\text{ km}. The distance from Venus to the Sun is 115\,000\,000\text{ km}.
What is the angle \theta, from Venus to the Sun to Mercury? Round your answer to the nearest minute.
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. Round your answer 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.
From the top of a rocky ledge 188 \text{ m} high, the angle of depression to a boat is 13 \degree. If the boat is d \text{ m} from the foot of the cliff find d correct to 2 decimal places.
Buzz is standing 49 \text{ m} from a building and measures the angle of elevation of the top of the building to be 23 \degree.
If the difference in height between the top of the building and Buzz's eye is h \text{ m} , find h correct to 2 decimal places.
If Buzz's eye is 135 \text{ cm} from the ground, what is the height of the building? Give your answer correct to one decimal place.
Lisa is on a ship and observes a lighthouse on a cliff in the distance. The base of the cliff is 906 \text{ m} away from the ship, and the angle of elevation of the top of the lighthouse from Lisa is 16 \degree.
If the top of the lighthouse is x \text{ m} above sea level, find x correct to 2 decimal places.
If the lighthouse is 21 \text{ m} tall, how tall is the cliff? Round your answer correct 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.
Consider the following diagram:
Find the following to two decimal places:
y
w
Hence, find x. Round your answer to one decimal place.
Consider the following diagram:
If \angle EBA is 60 \degree, name two other angles that are also 60 \degree.
Given that CD has a length of 5 \sqrt{7}, calculate the exact values of m \text{ and }n.
Consider the figure shown:
Find the exact length of the following:
p
q
r
s
Hence, find the exact perimeter of the quadrilateral.
Consider the given shape:
Find x.
Find the exact value of y.
Hence, find the exact perimeter of the shape.
A fighter jet, flying at an altitude of 2000 \text{ m} is approaching an airport. The pilot measures the angle of depression to the airport to be 13 \degree. One minute later, the pilot measures the angle of depression again and finds it to be 16 \degree.
Find the distance AC, to the nearest metre.
Find the distance BC, to the nearest metre.
Hence, find the distance covered by the jet in that one minute, to the nearest metre.
A jet takes off and leaves the runway at an angle of 34 \degree. It continues to fly in this direction for 7 \text{ min} at a speed of 630 \text{ km/h} before levelling out.
Find the distance covered by the jet just before levelling out in metres.
If the height of the jet just before levelling off is h \text{ m}, calculate h. Round your answer to the nearest metre.
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.
