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WAEC Mathematics 2016 Paper

Question : 48

Total: 49

An object is 6m away from the base of a mast. If the angle of depression of the object from the top of the mast is 50^o, find, correct to 2 decimal places, the height of the mast.

8.60m
7.83m
7.51m
7.15m

Validate

Solution:

Concept:

The angle of depression from the top equals the angle of elevation from the object to the top by alternate angles. Use the tangent ratio in the right triangle formed.

Explanation:

Let the height of the mast be

h

metres.

The object is

6

m from the base of the mast.

So the horizontal distance in the right triangle is

6

By alternate angles,

\tan 50^\circ = \frac{h}{6}

Therefore,

h = 6 \tan 50^\circ

Since

\tan 50^\circ \approx 1.19175

h = 6 \times 1.19175 = 7.1505

Correct to 2 decimal places,

h = 7.15

Answer:

7.15

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