SOLUTION: Ava wants to find the height of a flagpole. She determines that the angle of elevation to the top of the flagpole is 37o. She moves 15 feet closer and determines that the angle

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Question 1120573: Ava wants to find the height of a flagpole. She determines that the angle of elevation to the top of the flagpole is 37o. She moves 15 feet closer and determines that the angle of elevation is now 59o. Ava's eyes are 5.3 feet above the ground.
How tall is the flagpole? Round your answer to two decimal places.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Ava wants to find the height of a flagpole.
She determines that the angle of elevation to the top of the flagpole is 37o. She moves 15 feet closer and determines that the angle of elevation is now 59o.
Ava's eyes are 5.3 feet above the ground.
How tall is the flagpole? Round your answer to two decimal places.
:
Two right triangles are formed, top of flag pole, 5.3' above ground on the pole, and the observer
Use the tangent of the angles 37 and 59 degrees, the side opposite is the same for both triangles and is the height of the pole - 5.3' (h)
let x = the distance from the closer observation point, to the pole
then
(x+15) = the distance from the further observation point to the pole
tan(37) =
h = tan(37)*(x+15)
and
tan(59) =
h = tan(59)*x
:
h = h so we can write the equation and solve for x
tan(59)x = tan(37)(x+15)
x =
find the tangents and divide
x = .4528(x+15)
x = .4528x + 6.792
x - .4528x = 6.792
.5472x = 6.792
x =
x = 12.4 ft
therefore
h = tan(59)*12.4
h = 20.657 + 5.3 = 25.96 ft is the height of he flag pole
:
;
Check using the other angle
h = tan(37)(12.4+15)
h = 20.65 + 5.3 = 25.95 ft, very close