Question

PRECALCULUS QUESTION PLEASE HELP!!!!!!

1. What is the tangent of angle Y?

A. tan Y= y/z
B. tan Y = x/z
C. tan Y = z/y
D. tan Y = y/x

Answer 1

A. tan Y= y/z
Just remember the three major identities for trig with a right triangle.
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
And in the diagram, the opposite side to Y is y and the adjacent side is z. So the tangent is y/z which matches option "A" from your choices.

Answer 2

By definition you have that the tangent of an angle in a right triangle is given by the quotient between the sine of the angle and the cosine of the angle.
Since we know how much the sine and the cosine measure (we have the sides of the triangles as data), then the tangent is given by:
A. tan Y= y/z
answer
A. tan Y= y/z