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Year 10 Interactive Maths - Second Edition


Problem Solving

The solution to many practical problems in navigation, surveying, engineering and geography involves solving a triangle problem.  In this section, we will restrict the problems to those that involve right-angled triangles.


Example 14

Solution:

Let the height of the gate be h m.

In the right-angled triangle ABC,

So, the gate is 3.95 m high.


Example 15

A surveyor measures the angle to the peak of a hill from point A, as shown in the diagram. Calculate the height, h, of the hill rounded to 2 decimal places.

Solution:

In the right-angled triangle ABC,

So, the height of the hill is 113.03 m.


Angle of Inclination

The angle of inclination is the angle made by an object with the horizontal (or vertical) as described by the situation.


Example 16

A ladder 5 m long has its end just resting on the top of a fence 3 m high. What angle, to the nearest minute, does the ladder make with the ground?

Solution:


Key Terms

angle of inclination


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