A 40-foot T.V. antenna stands on top of a building. From a point on the ground, the angle of elevation to the top and to the bot
tom of the antenna measures 56° and 42° respectively. How tall is the building?
1 answer:
Answer:
61.5
Step-by-step explanation:
In this case to calculate the height, we do the following:
The first is the graphic, attached image.
Then the calculations.
b / d = tan (42 °) = 0.9
d = b / 0.9
Then we have to:
(40 + b) / d = tan (56 °) = 1.48
(40 + b) = d * 1.48
Replacing we have:
(40 + b) = (b / 0.9) * 1.48
40 + b = 1.65 * b
1.65 * b - b = 40
b = 40 / 0.65
b = 61.5
Therefore the height is approximately 61.5
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