In a 125-ft tall building, if you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°, the height of the antenna is 21.7 ft.
In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
We will use the tangent of 68°, being the height of the building (h1 = 125 ft) the opposite side.
tan 68° = 125 ft / x
x = 50.5 ft
We will use the tangent of 71°, being the distance to the building (x = 50.5 ft) the adjacent side.
tan 71° = h2 / 50.5 ft
h2 = 146.7 ft
h2 - h1 = 146.7 ft - 125 ft = 21.7 ft
In a 125-ft tall building, if you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°, the height of the antenna is 21.7 ft.
The complete question is:
You want to measure the height of an antenna on the top of a 125 foot building. From a point in front of the building, you measure the angle of elevation to the top of the building to be 68° and the angle of elevation to the top of the antenna to be 71°. How tall is the antenna, to the nearest tenth of a foot?
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