Question

Lin is playing hand ball and wants the ball to bounce off wall CB and land at D. Where on the wall should she aim if she's standing at point A?
A. 7.8 feet away from point B
B. 13.3 feet away from point B
C. Anywhere along the wall since all of the triangles will be similar ​

Answer 1

The triangles formed by the path of the ball and the wall in the given diagram are similar triangles.

Correct Response;

The point on the wall she should aim is; A. 7.8 feet away from point B

Method by which the above value is obtained;

The possible diagram in the question is attached

Let x represent the distance from point B where the ball lands.

ΔCDE is similar to ΔABE, by Angle-Angle similarity postulate.

By trigonometric ratio, the tangent of the angles ∠CDE and ∠BAE are;

$tan(\angle CDE) = \mathbf{\dfrac{20 - x}{25}}$

$tan(\angle BAE) = \mathbf{ \dfrac{x}{16}}$

tan(∠CDE) = tan(∠BAE)

Therefore;

$\dfrac{20 - x}{25} = \dfrac{x}{16}$

Which gives;

16 × (20 - x) = 25·x

320 = 41·x

x = 320 ÷ 41 ≈ 7.8

The point on the wall she should aim if she's standing at point A is therefore;

• A, 7.8 feet away from point B

Learn more about trigonometric ratios here:

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