Question

Sean and Jackie made a shady area by stretching a bedspread over a clothesline. the bedspread was 2.4 m long and made an angle of 52 degrees with the ground where it was anchored at each side. How wide was the shady area?

Answer 1

This one is cos 52 = a/2.4
a = 2.4 cos 52
a = 1.477 m long shadow

Answer 2

1.47 m

Explanation:

Given: The bedspread was 2.4 m long and made an angle of 52 degrees with the ground where it was anchored at each side.

To Find: How wide was the shady area?

Solution:

Refer the attached figure.

The bedspread was 2.4 m long i.e.AC = 2.4 m

The bedspread made an angle of 52 degrees with the ground i.e.∠ACB = 52°

Now we are supposed to find the width of shady area .i.e. BC

We will use trigonometric ratio.

In ΔABC

`Cos \theta = (Base)/(Hypotenuse)`

`Cos 52^(\circ) = (BC)/(AC)`

`Cos 52^(\circ) = (BC)/(2.4)`

`0.61566 = (BC)/(2.4)`

`2.4 * 0.61566 =BC`

`1.4775 =BC`

Hence the width of the shady area is 1.47 m