Saul is on his kayak paddling through the Colorado River instead of taking his Geometry test. He spots the Hoover Dam ahead of him at an angle of elevation of 42°. If the dam stands 761 feet above his viewing point, what is the horizontal distance from Saul to the dam. (10 pints for best answer)
Answers
Given : Saul is on his kayak paddling through the Colorado River instead of taking his Geometry test. He spots the Hoover Dam ahead of him at an angle of elevation of 42°.
the dam stands 761 feet above his viewing point,
To Find : horizontal distance from Saul to the dam
Solution:
Angle of elevation = 42°
Dam height = 761 feet
Horizontal distance = x feet
Tan Angle of elevation = Dam height/Horizontal distance
=> Tan 42° = 761 / x
=> x = 761 / Tan 42°
=> x = 761/0.9
=> x = 845.55 feet
horizontal distance from Saul to the dam = 845.55 feet
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Given :- (from image)
- AB = 761 feet .
- ∠ACB = 42° .
To Find :-
- BC = ?
Solution :-
In right angled ∆ABC,
→ tan 42° = Perpendicular / Base
→ tan 42° = AB / BC
→ tan 42° = 761 / BC
→ 0.9 = 761 / BC
→ BC = 761 / 0.9
→ BC ≈ 845.6 feet . (Ans.)
Hence, the horizontal distance from Saul to the dam is 845.6 feet .
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