Question

The angle of elevation to the top of a building in seattle is found to be 2 degrees from the ground at a distance of 2 miles from the base of the building. Using this information, find the height of the building.

Answer 1

Explanation:

This problem can be set up as a right triangle where the tall side (height of the building) is an unknown variable (x) and the base of the triangle is 1 mile. The angle opposite of the tall side, x, is 7 degrees.

Now you can use the tangent trig function whereby tan(angle) = opposite length /adjacent length. Opposite length is x, adjacent length is 1 mile, angle is 7 degrees.

tan(7º) = x / 1

rearrange for x

x = 1*tan(7º) = ~ 0.123 miles. (make sure to use degree mode on your calculator when calculating the tangent)

Now to get feet, just multiply by 5,280 ft in one mile

Height of the building is .123 miles * 5280 ft/mile = 649.44 ft