Answer:
Therefore, the length of YZ = 12
Step-by-step explanation:
As we know that
sin(X) = Opposite ÷ Hypotenuse
cos(X) = Adjacent ÷ Hypotenuse
tan(X) = Opposite ÷ Adjacent
Given the ratios
sin(X) = 12 ÷ 13 = Opposite ÷ Hypotenuse
cos(X) = 5 ÷ 13 = Adjacent ÷ Hypotenuse
tan(X) = 12 ÷ 5 = Opposite ÷ Adjacent
As
tan(X) = Opposite ÷ Adjacent
In the shown diagram,
- the opposite of tan(X) = YZ, and
- the adjacent of tan(X) = XY
also the given ratio is
tan(X) = 12 ÷ 5
so
tan(X) = YZ ÷ XY
= 12 ÷ 5 ∵ YZ = 12, and XY = 5
Therefore, the length of YZ = 12
