You see a distant office tower that you know to be 860 feet tall. If you measure its angular size to be 3.5 degrees, how far away from the building are you

Question

Mathematics

Nathanael Cooley

23 September, 20:53

You see a distant office tower that you know to be 860 feet tall. If you measure its angular size to be 3.5 degrees, how far away from the building are you

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Jacoby Barrett · Answer 1

The given angular size of the building can also be reported as the angle of elevation. In the triangle formed by the edges of the parameters given, the distance from the person to the building is the adjacent side of the triangle and the opposite side is given to be 860 feet.

Let the unknown distance be x. The trigonometric function that allows us to solve the unknown is,

tan (3.5 °) = 860 ft / x ft

0.06116 = 860 ft / x ft

The value of x from the equation is 14060.88.

Hence, the person is 14060.88 ft away from the building.