Question

HELP PLS!!

Find the value of x and the value of y.
A. x = 16, y = 9√2
B. X= 7, y = 16√2
C. x = 6√2, y=7√2
D. X= 7√3, y = 16

Answer 1

A

Explanation:

Completing the rectangle formed by legs 9 and 7 , gives us a right triangle on the left.

Using the sine ratio and the exact value sin45° =
`(1)/(√(2) )` , then

sin45° =
`(opposite)/(hypotenuse)` =
`(9)/(y)` =
`(1)/(√(2) )` ( cross- multiply )

y = 9
`√(2)`

Using the tan ratio in the right triangle and the value tan45° = 1 , then

tan45° =
`(opposite)/(adjacent)` =
`(9)/(adj)` = 1

adj = 9

Then

x = 9 + 7 = 16

Answer 2

A

Explanation:

Thanks to the given angle, we can say that the triangle formed by tracing another height has two congruent legs

So

x = 9 + 7 = 16

y = √2 * 9^2 = 9√2