Answer:
[tex]\boxed{h=60.1\ ft }[/tex]
Step-by-step explanation:
Right Triangles
They have a right angle (90°) and a longer side called the hypotenuse opposite to the right angle. The legs and the hyponetuse form two angles that must sum 90°, and they comply:
[tex]\displaystyle sin\ \alpha=\frac {opp-leg}{hypotenuse}[/tex]
Where opp-leg is the opposite leg to [tex]\alpha.[/tex]
The rope from the top of a tree house is 85-foot long. It's the hypotenuse (L) of the triangle it forms with the ground and the tree. The angle of 45° is opposite to the height of the tree (h).
[tex]\displaystyle sin\ \alpha=\frac {h}{L}[/tex]
We can solve for h
[tex]h=L\ sin\alpha =85\ sin\ 45^o[/tex]
[tex]\boxed{h=60.1\ ft }[/tex]
