Question

Find the height of the basketball hoop to the nearest foot.

A. 7 ft
B. 10 ft
C. 12 ft
D. 15 ft

Answer 1

12 ft

Explanation:

Hi there!

1) Find the length of the other leg in the right triangle

There are two ways we can go about this. The first way is to use trigonomic ratios:

We're given one of the legs and we're trying to solve for the other, so we can use the tangent ratio:

`tan\theta=(opp)/(adj)`

Let x be equal to the length of the other leg. Plug in the known values:

`tan45=(x)/(7)\\7*tan45=x\\x=7`

The other way to find this is to observe the angles. Because we're given that two of the angles are 45 and 90 degrees, we know that the third angle is 45 degrees. This makes this an isosceles triangle, meaning the other leg is 7 ft long.

2) Determine the height of the hoop

Add 7 ft and 5 ft (the person's height):

7+5=12 ft

I hope this helps!