Question

Find the value of the variable. If your answer is not an integer, leave it in simplest radical form.

A. 7
`√(2)`
B.
`(7√(3) )/(2)`
C.
`7√(3)`
D.
`(7√(2) )/(2)`

Answer 1

`\large \boxed{\mathrm{D. \ \displaystyle (7√(2) )/(2 )}}`

Explanation:

The triangle is a right triangle.

We can use trigonometric functions to solve the problem.

`sin \theta = opp/hyp`

The opposite side to the angle 45 degrees is x and the hypotenuse of the triangle is 7.

`sin 45 = x/7`

Multiply both sides of the equation by 7.

`7 sin 45 = x`

Simplify the value.

`\displaystyle (7√(2) )/(2 )=x`

Answer 2

7 sqrt(2)/2 =x

Explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 45 = x/7

7 sin 45 =x

7 sqrt(2)/2 =x