Question

Use the picture below to answer the question.

6 ft
The angle of elevation from the swimmer to the lifeguard is 35*
Find the distance x from the swimmer to the base of the lifeguard chair.
Find the distance y from the swimmer to the lifeguard.
Round to the nearest tenth as needed.
Select the correct response
x=7.3ft, y= 3.4ft
x=8.6 ft y=10.5 ft
x=3.4ft, y=73 ft
x=10.5 ft, y= 8.6 ft

Answer 1

Answer: x = 8.6 y=10.5

Explanation:

1. This is a question about trig identities, familiarize yourself with sin, cos, tan
2. In this problem, our value for degrees is 35 and our opposite side is 6ft
3. Our variables to solve are x and y, x being the adjacent size and y being the hypothenuse
4. y has to be the longest size, it being the hypothenuse, so eliminate the first and last options
5. tan = opposite/adjacent so, tan(35)=6/x.
6. solve this equation for x, yielding 8.6
7. For y, using the fact that sin=opposite/hypothenuse
8. substitute and get the equation sin(35)=6/y
9. solve and get y =10.5
10. x=8.6 and y= 10.5