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?