Question

A right triangle has an angle that measures 34 and the adjacent side measures 17. What is the length of the hypotenuse to the nearest tenth

Answer 1

We are including the adjacent and hypotenuse, so we will be using cos.
\[\cos 34 = \frac{ adjacent }{ hypostenuse }\]
\[\cos 34 = \frac{17}{?}\]
Now move the unknown hypotenuse to the other side:
\[(x)(\cos 34) = 17\]
\[\cos 34 \approx 0.83\]
\[(x)(0.83) = 17\]
Now divide the cos 34 on both sides:
\[\frac{ (x)(0.83) }{ 0.83 } = \frac{ 17 }{ 0.83}\]
\[x \approx 20.48\]

Answer 2

@Haliemichelle