A flagpole is situated at the top of a building 120 ft tall. From a point in the same horizontal plane as the base of the building, the angles of elevation of the top and bottom of the flagpole are 73.2° and 67.2°, respectively. How tall is the flagpole?
(Please help me)
Answers
Answer:
The height of the flagpole is approximately 60 feet.
Step-by-step explanation:
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
.
tan
42
˚
1
=
H
500
H
=
500
tan
42
˚
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
tan
38
˚
1
=
a
500
a
=
500
tan
38
˚
We can now state that
h
=
H
−
a
h
=
500
tan
42
˚
−
500
tan
38
˚
h
≈
59.559
≈
60
feet
Hopefully this helps!
Answer:
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Step-by-step explanation:
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