Question

need to find y hypotunse with 45 45 and 90 degree angles and a side length of 85

Answer 1

85√2.

1) Since we have a right triangle with two congruent angles, then we can find the hypotenuse by using a trigonometric ratio:

$\begin{gathered} \sin (45)=\frac{85}{y} \\ \frac{\sqrt[]{2}}{2}=\frac{85}{y} \\ y\sqrt[]{2}=170 \\ y=\frac{170}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ y=\frac{170\sqrt[]{2}}{2} \\ y=85\sqrt[]{2} \end{gathered}$

2) So the hypotenuse is 85√2

Another way to find that out is considering that the hypotenuse would be the diagonal of a square (since we have two 45º angles and one right angle (90º) and the diagonal of a square is a√2 then 85√2