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

Answer:

The building is 161.632 meters tall

Step-by-step explanation:

We could solve this multiple ways.

Using pythagorean theorem

$H^2+90^2=185^2\\H^2=34225-8100\\H^2=26125\\H = \sqrt{26125}\\H = 161.6322988$

Using angles

$cos(a) = \frac{90}{185}\\ a = cos^-^1(\frac{90}{185})\\a = 60.89$

$sin(60.89)=\frac{H}{185}\\ H = 185sin(60.89)\\H = 161.6321557$

Answer 2

Answer:

Height = 161.6 meters to the nearest tenth.

Step-by-step explanation:

Use the PythagorasTheorem:

185^2 = 90^2 + h^2

h^2 = 185^2 - 90^2

h^2 = 26125

h = 161.63 meters.