Question

Fill in the blank.

In the triangle below, x = _____ and y = _____. Round your answer to two decimal places.

Answer 1

Part 1)
`x=44.80\ units`

Part 2)
`y=56.85\ units`

Explanation:

Part 1) Find the value of x

we know that

In the right triangle of the figure

The tangent of angle of 52 degrees is equal to divide the opposite side to the angle of 52 degrees (x units) by the adjacent side to the angle of 52 degrees (35 units)

`tan(52\°)=x/35`

Solve for x

`x=(35)tan(52\°)`

`x=44.80\ units`

Part 2) Find the value of y

we know that

In the right triangle of the figure

The cosine of angle of 52 degrees is equal to divide the adjacent side to the angle of 52 degrees (35 units) by the hypotenuse (y units)

`cos(52\°)=35/y`

Solve for y

`y=35/cos(52\°)`

`y=56.85\ units`