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avanturin [10]
3 years ago
5

An 85-foot rope from the top of a tree house to the ground forms a 45 degree angle of elevation from the ground. How high is the

top of the tree house in feet?
Mathematics
1 answer:
Feliz [49]3 years ago
6 0

Answer:

\boxed{h=60.1\ ft }

Step-by-step explanation:

<u>Right Triangles </u>

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:

\displaystyle sin\ \alpha=\frac {opp-leg}{hypotenuse}

Where opp-leg is the opposite leg to \alpha.

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).

\displaystyle sin\ \alpha=\frac {h}{L}

We can solve for h

h=L\ sin\alpha =85\ sin\ 45^o

\boxed{h=60.1\ ft }

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