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)
Answers
Hailey's diving partner from the boat is at 288 ft
Step-by-step explanation:
boat is anchored 300 feet away at a 30° angle of depression
Cos 30 = Horizontal Distance of boat / 300 ft
=> √3 / 2 = Horizontal Distance of boat / 300 ft
=> Horizontal Distance of boat = 150√3 ft
Sin30 = Vertical Distance of boat / 300 ft
=> 1/2 = Vertical Distance of boat / 300 ft
=> Vertical Distance of boat = 150 ft
her diving partner is 25 feet directly below her
Hence her partner vertical Distance from boat = 150 - 25 = 125 ft
Her partner horizontal Distance from boat is same as her = 150√3 ft
Hailey's diving partner Distance from the boat = √(125)² + (150√3)²
= 25 √(25 + 108)
= 25√133
= 288.3
= 288 ft
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