find the height of the building

Question

The angle of elevation to the top of a building in a city is found to be 3 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. (Round your answer to four decimal places.)

Answer 1

First make a right triangle with base of 2 miles and an altitude of h, which is the height of the building.

Now the tangent of 3 degrees in this triangle is h/2. So you can solve for h is you know the value of the tangent.

Using my calculator I get Tan 3 degrees is 0.052. Plug in and solve for h getting 0.105. miles

Of course height of buildings is not measured in miles,, so multiply by 5280 to get h 553,4 feet.

Answer 2

Given:

angle of elevation (a) = 3 degrees

distance from the building (d) = 2 miles = 2 x 5280 = 10,560 feet

Required:

height of the building (h) = ?

Solution

tan (a) = h / d

tan 3 = h / 10560

h = 10560 tan 3 = 10560 x 0.05240778

h = 553.4262 feet

Answer 3

tan 3 = x/2

2 * tan 3 = x <--- this is in miles

the building is 553 feet 5 and 1/8 inches tall

Answer 4

With respect to the angle, you are trying to find the opposite side, given the angle and the adjacent side. You would use tangent. (tan = opposite/adjacent)

Let x = height of the building

tan 3 = x/2 Multiply both sides by 2

2 tan 3 = x

x=.105 miles