# math

Hailey is scuba diving in the ocean. Her boat is anchored 300 feet away at a 30° angle of depression. If her diving partner is 25 feet directly below her, how far is Hailey's diving partner from the boat? (round to nearest whole number)
a. 300 ft
b. 313 ft
c. 325 ft
d. 326 ft ****

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1. Assuming the 300 ft is the direct distance, (hypotenue),
let the horizontal distance be x
cos30 = x/300
x = 300cos30
Hailey's vertical depth:
y/300 = sin30
y = 300sin30 = 150
So partner's depth = 150+70 = 220 ft
partner's distance form boat: z
z^2 = x^2 + y^2

etc

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posted by Reiny
2. sinΘ =
opp
hyp

Hailey's depth: x = 300sin30 = 150

partner's depth = 150 + 25 = 175

then, find horizontal distance

3002 = 1502 + b2
b = 150
3

then,

c2 = (150
3
)2 + (175)2
c = 313.25

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3. Hailey is scuba diving in the ocean. Her boat is anchored 300 feet away at a 30° angle of depression. If her diving partner is 25 feet directly below her, what is the angle of depression from the boat to Hailey's diving partner? (round to nearest whole number)

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