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WAEC Mathematics 2011 Paper

Question : 35

Total: 47

a boy looks through a window of a building and sees a mango fruit on the ground 50m away from the foot of the building. If the window is 9m from the ground, calculate, correct to the nearest degree, the angle of depression of the mango from the window

9^o
10^o
11^o
12^o

Validate

Solution:

Concept:

The angle of depression is the angle between the horizontal line from the window and the line of sight to the mango. Use the tangent ratio in the right triangle formed.

Explanation:

The window is

9

m above the ground, and the mango is

50

m from the foot of the building. So, the vertical drop is

9

m and the horizontal distance is

50

Thus,

\tan \theta = \frac{\text{vertical drop}}{\text{horizontal distance}} = \frac{9}{50} = 0.18

So,

\theta = \tan^{-1}(0.18)

Calculating,

\theta \approx 10.20^\circ

Correct to the nearest degree,

\theta \approx 10^\circ

Answer:

10^\circ

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