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 stand

Question

2 years ago

15

ing 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

1 answer:

ASHA 777 [7] · Answer 1 · 2023-01-17T23:38:09+03:00

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

<h3>Correct Response;</h3>

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

<h3 /><h3>Method by which the above value is obtained;</h3>

The possible diagram in the question is attached

Let <em>x</em> represent the distance from point <em>B</em> 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 <em>A</em> is therefore;

Learn more about trigonometric ratios here: