Answer:
The height of tree house is 70.71 feet
Step-by-step explanation:
We are given that A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground
Refer the attached figure
Length of rope AC = Hypotenuse =100 feet
The top of a tree house to the ground forms a 45∘ angle of elevation from the ground =[tex]\angle ACB = 45^{\circ}[/tex]
We are supposed to find the height of tree house i.e.AB = Perpendicular
So, Using trigonometric ratio
[tex]Sin \theta = \frac{perpendicular}{Hypotenuse}\\Sin 45= \frac{AB}{AC}\\\frac{1}{\sqrt{2}}=\frac{AB}{100}\\100 \times \frac{1}{\sqrt{2}}=AB\\70.71=AB[/tex]
Hence The height of tree house is 70.71 feet
