The angle of depression from a lifeguard in her chair to a person swimming in a pool is 38 degrees. If the height of the chair is 12 feet tall, find the distance from the base of the lifeguard's chair to the swimmer.

15.36 feet

Step-by-step explanation:

We solve the above question using Trigonometric function of Tangent

Tan θ = Opposite /Adjacent

From the question

θ = 38°

Opposite = the height of the chair = 12 feet tall

Adjacent = the distance from the base of the lifeguard's chair to the swimmer = x

Hence:

tan 38° = 12/x

Cross Multiply

tan 38° × x = 12

x = 12/tan 38°

x = 15.359299586

x ≈ 15.36 feet

Hence, the distance from the base of the lifeguard's chair to the swimmer is 15.36 feet

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47