There are many diff erent types of clinometer. A very simple type is shown in the diagram on the right.
Answering ‘real world’ problems 1
3 5
If necessary, draw a sketch to represent the situation given. Label the sides of the triangle.
Solve the equation to fi nd the unknown angle or side.
2 4
tube/pipe/drinking straw view through here protractor
Identify the angle given or required.
Use the ‘we have, we have, we want’ strategy to form an equation.
required angle
string and weight
Discuss and discover
Work with a partner to make a clinometer and use it to measure the height of something in your school grounds.
Worked example 1 A squirrel is sitting on the forest fl oor and looks up at an acorn at the top of a tree.
If he looks up at an angle of 26° and he is sitting 15 m from the base of the tree, how tall is the tree, to the nearest metre?
Solution A
opp hyp 26°
15 m adj
Worked example 2
A man standing on a cliff sees a boat at an angle of depression of 36°. If the cliff is 65 m tall, how far from the cliff is the boat? Give your answer correct to one decimal place.
Solution M
36°
65 m adj
90 – 36 = 54°
hyp B X opp Section C Applying our skills 551
The angle of depression is outside the triangle. To fi nd the angle inside, subtract it from 90°