Question

The length of the hypotenuse in a 45°-45°-90° triangle is 11 ft. What is thelength of a leg?

Answer 1

Answer:

The length of each of the remaining two legs is 7.78 ft

Explanations:

The diagram below illustrates the given description

$\begin{gathered} \cos \text{ }\theta\text{ = }\frac{\text{Adjacent}}{\text{Hypotenuse}} \\ \cos \text{ 45 = }\frac{Adjacent}{11} \\ \text{Adjacent = 11 }\cos 45 \\ \text{Adjacent = }0.707\text{ }(11) \\ \text{Adjacent = }7.78 \end{gathered}$$\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ \sin \text{ 45 = }\frac{Opposite}{11} \\ \text{Opposite = 11 sin 45} \\ \text{Opposite = }11\text{ (0.707)} \\ \text{Opposite = 7.78} \end{gathered}$

The length of each of the remaining two legs is 7.78 ft