Question

Jacob lives in an apartment. He has to tie an 185-meter long rope at the distance of 90 meter from the building to its roof. What is the height of the building?

Answer 1

Height = 161.6 meters to the nearest tenth.

Explanation:

Use the PythagorasTheorem:

185^2 = 90^2 + h^2

h^2 = 185^2 - 90^2

h^2 = 26125

h = 161.63 meters.

Answer 2

The building is 161.632 meters tall

Explanation:

We could solve this multiple ways.

Using pythagorean theorem

`H^2+90^2=185^2\\H^2=34225-8100\\H^2=26125\\H = √(26125)\\H = 161.6322988`

Using angles

`cos(a) = (90)/(185)\\ a = cos^-^1((90)/(185))\\a = 60.89`

`sin(60.89)=(H)/(185)\\ H = 185sin(60.89)\\H = 161.6321557`