LABELLING RIGHT ANGLED TRIANGLES WORKSHEET

In the diagrams below, name the:

i) Hypotenuse

ii)  Side opposite the angle marked θ

iii) Side adjacent to the angle marked θ.

Problem 1:

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

The right angled triangle alongside has hypotenuse of length a units and other sides of length b units and c units. θ and Φ are the two acute angles. Find the length of the side:

a)   Opposite θ

b)   Opposite Φ

c)   Adjacent to θ

d)   Adjacent to Φ

Solution

Problem 5 :

Given the right angle triangle shown here:

state the length of :

1) the side opposite angle a

2) the side opposite angle b

3) the hypotenuse

4) the side adjacent to angle b 

5) the side adjacent to angle a

Solution

Problem 6 :

Given the right angle triangle ABC shown here

name the:

1) Hypotenuse

2) Adjacent side to b

3) Opposite side to a

4) Opposite side to b

5) Adjacent side to a

Solution

Problem 7 :

You are measuring the height of a spruce tree. You stand 45 feet from the base of the tree. You measure the angle of elevation from the ground to the top of the tree to be 59°. Find the height h of the tree to the nearest foot.

Solution

Problem 8 :

The backboard of the basketball hoop forms a right triangle with the supporting rods, as shown. Use the Pythagorean Theorem to approximate the distance between the rods where they meet the backboard.

Solution

Problem 9 :

The fire escape forms a right triangle, as shown. Use the Pythagorean Theorem to approximate the distance between the two platforms.

Solution

Problem 10 :

The top of the slide is 12 feet from the ground and has an angle of depression of 53°. What is the length of the slide?

Solution

Problem 11 :

The angle between the bottom of a fence and the top of a tree is 75°. The tree is 4 feet from the fence. How tall is the tree? Round your answer to the nearest foot.

Solution

Problem 12 :

An anemometer is a device used to measure wind speed. The anemometer shown is attached to the top of a pole. Support wires are attached to the pole 5 feet above the ground. Each support wire is 6 feet long. How far from the base of the pole is each wire attached to the ground?

Solution

Calculate the angle θ in each of the following triangles. In each case give your answer correct to 1 decimal place.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

The diagram shows the cross section of the shed. Calculate the angle θ between the roof and the horizontal. Give your answer to the nearest degree.

Problem 4 :

The ladder of length 6 m leans against a wall. The foot of the ladder is at a distance of 3 m from the base of the wall. Calculate the angle between the ladder and the ground.

Solution

Problem 5 :

You are measuring the height of a lamppost. You stand 40 inches from the base of the lamppost. You measure the angle of elevation from the ground to the top of the lamppost to be 70°. Find the height h of the lamppost to the nearest inch

Solution

Problem 6 :

Describe the error in the statement of the tangent ratio. Correct the error if possible. Otherwise, write not possible.

Solution

Problem 7 :

Describe the error in the statement of the tangent ratio. Correct the error if possible. Otherwise, write not possible.

Solution

Problem 8 :

A surveyor is standing 118 feet from the base of the Washington Monument. The surveyor measures the angle of elevation from the ground to the top of the monument to be 78°. Find the height h of the Washington Monument to the nearest foot.

Solution

Problem 9 :

Scientists can measure the depths of craters on the moon by looking at photos of shadows. The length of the shadow cast by the edge of a crater is 500 meters. The angle of elevation of the rays of the Sun is 55°. Estimate the depth d of the crater.

Solution

Problem 10 :

Your family room has a sliding-glass door. You want to buy an awning for the door that will be just long enough to keep the Sun out when it is at its highest point in the sky. The angle of elevation of the rays of the Sun at this point is 70°, and the height of the door is 8 feet. Your sister claims you can determine how far the overhang should extend by multiplying 8 by tan 70°. Is your sister correct? Explain.

Solution

Problem 11 :

You are skiing on a mountain with an altitude of 1200 feet. The angle of depression is 21°. Find the distance x you ski down the mountain to the nearest foot.

Solution