A sonar operator on a cruise detects a submarine at a distance of 500 m and an angle of depression of 37°. How deep is the submarine, to the nearest meter?

Question

options

A: 656

B: 831

C: 301

D: 399

Answer 1

construct a right triangle, base = 500, angle = 37 degrees

opposite side = 500tan37 = about 376.8 meters

but the 500 probably refers to the hypotenuse of a right triangle,

then depth = d = opposite side = 500sin37 = 301 meters, c appears to be the correct answer

choices:

a 656

b 831

c 301

d 399

500sin37 = 301 meters

500cos37 = 399

500/tan37 = 663

500/cos37 = 626

if depth were the adjoining side of the right triangle, then

d = 500cos37 = 399

500/sin37 = 500csc37 = 831

500tan37 = 377

not being familiar with how sonar works, you could still eliminate option "a" as not fitting any of the possible right angle constructions. b seems unlikely. leaving c or d. c seems more reasonable than d.