Question

Use special right triangle ratios to find the length of the hypotenuse.OA. 30O B. 15√/3O C. 15O D. 15√/245°1545

Answer 1

Given:

The given triangle is right angled triangle.

The angle is 45 degrees.

The adjacent side is 15.

Required:

We need to find the hypotenuse of the given triangle.

Step-by-step explanation:

Consider the cosine formula.

`cos\theta=\frac{adjacent\text{ side}}{hypotenuse}`
`Substitute\text{ }\theta=45\degree\text{ and adjacent side=15 in the formula.}`
`cos45\degree=(15)/(hypotenuse)`
`hypotenuse=(15)/(cos45\degree)`
`Use\text{ }cos45\degree=(√(2))/(2)\text{ in the equation.}`
`hypotenuse=(15)/((√(2))/(2))`
`hypotenuse=15*(2)/(√(2))`
`hypotenuse=15*(√(2)*√(2))/(√(2))`
`hypotenuse=15*√(2)`
`hypotenuse=15√(2)`

Final answer:

`hypotenuse=15√(2)`