Question

Analyze the diagram below and complete the instructions that follow.Find the value of x and the value of y.

Answer 1

A

Explanation:

Drawing a segment from the left side of the top base to the lower base, creates a right triangle on the left with legs 9 and x₁ and hypotenuse y

Using the tangent ratio in the right triangle and the exact value

tan45° = 1 , then

tan45° =
`(opposite)/(adjacent)` =
`(9)/(x_(1) )` = 1, so x₁ = 9 and

x = 7 + x₁ = 7 + 9 = 16

Using the sine ratio in the right triangle and the exact value

sin45° =
`(1)/(√(2) )` , then

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

y = 9
`√(2)`