A flagpole sits on the top of a building. Angles of elevation are measured from a point 500 feet away from the building. The angle of elevation to the top of the building is 38˚ and to the top of the flagpole 42˚. How high is the flagpole?

2 Answers
Apr 10, 2017

The height of the flagpole is approximately 60 feet.

Explanation:

Always try to draw a diagram.

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We know that there is a right angle between the ground and the building. Therefore, we can use the 3 basic trig ratios instead of the sine or cosine law to solve this problem.

Since the angle in the corner of the larger right triangle measures 42˚, the top angle in this triangle measures 180˚ - 90˚ - 42˚ = 48˚.

By basic trig ratios, we can find the height of the building with the flag pole on top, call it H.

(tan42˚)/1 = H/500

H = 500tan42˚

I would keep it in exact form until the last step.

We now devise an expression for the height of the building (without the flag pole). Call it a

(tan38˚)/1 = a/500

a = 500tan38˚

We can now state that

h = H - a

h = 500tan42˚ - 500tan38˚

h ~~ 59.559 ~~ 60 "feet"

Hopefully this helps!

Apr 10, 2017

The flagpole is 60ft in height to the nearest foot.

Explanation:

1) The flagpole is on top of a building.
2)Angles of elevation both measured from point 500ft from building
3) Angle of elevation to the top of building is 38deg
4) Angle of elevation to the top of flagpole is 42deg

The information above will provide us with two right angle triangles, one smaller one inside a larger one.

Both will have a base of 500ft.

The smaller triangle will have a base angle beta of 38deg opposite the 90deg, and the larger triangle will have a base angle beta of 42deg.

From this information we can find the heights of the building and the building + pole using the definition of the tangent of the two base angles beta:

tan(beta)=(opp)/(adj) where the opp is the height and the adj is the 500ft

opp(build)=tan(38)*(500ft)=390.6ft=height of building

opp(flag)=tan(42)*(500ft)=450.2ft=height of building + pole

Then to the nearest foot the height of the flagpole is:

450.2ft-390.6ft=60ft