SOLUTION: I need help with these three problems 1. The angle of elevation from a point on the ground to the top of a building is 35 degrees. If the point on the ground is 150 ft from the

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Question 1137114: I need help with these three problems
1. The angle of elevation from a point on the ground to the top of a building is 35 degrees. If the point on the ground is 150 ft from the building, how tall is the building?


The building is feet tall.

2.
A boat is spotted from the top of a 15 ft lighthouse at an angle of depression of 20 degrees. How far from the base of the lighthouse is the boat to nearest tenth?


The boat is feet away from the base of the lighthouse.



3.
A ramp rises 1 ft for every 7 ft horizontal. What angle, to the nearest degree, does the ramp make with the ground?


The ramp makes a degree angle from the ground.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
here's my worksheet.

$$$

in problem 1, x is the height of the building.

tan(35) = x / 150

solve for x to get x = 150 * tan(35) = 105.0311307 feet.

rounded to the nearest tenth of a foot, it's 105 feet.

rounded to the nearest hundredth of a foot, it's 105.03 feet.

in problem 2, x is the distance from the lighthouse.

the angle of depression is 20 degrees.

a right triangle is formed where the vertical distance is 15 and the horizontal distance is x.

the top angle of the triangle is 70 which makes the bottom right angle equal to 20 degrees.

tan(20) = 15 / x

solve for x to get x = 15 / tan(20) = 41.21216129 feet.

round to nearest tenth to get 41.2 feet.

round to nearest hundredth to get 41.21 feet.

in problem 3, the horizontal distance is 7 and the vertical distance is 1.

x is the angle of elevation from the ground.

tan(x) = 1/7.

solve for x to get x = arc tangent (1/7) = 8.130102354 degrees

round to nearest tenth to get 8.1 degrees.

round to nearest hundredth to get 8.13 degrees.