SAT Right Triangles & Trigonometry Question 44 | Free SAT Prep

00:00

Try Full-Screen!

Question 44·Medium·Right Triangles and Trigonometry

0 / 50

In right triangle $XYZ$ , angle $Z$ is the right angle. If $\sin X = \dfrac{4}{7}$ , what is $\tan Y$ ?

When a sine value is given in a right triangle, treat it as opposite over hypotenuse. Assign proportional side lengths, find the third side with the Pythagorean theorem, then form the requested tangent ratio from opposite over adjacent.

Hints

Click me!

Use the sine ratio

Since sin X is opposite over hypotenuse, label the side opposite X as 4 parts and the hypotenuse as 7 parts.

Find the third side

Use the Pythagorean theorem with one leg 4 and hypotenuse 7.

Use tangent for angle Y

For angle Y, tangent is the side opposite Y divided by the side adjacent to Y.

Step-by-step Explanation

Label sides from the sine ratio

Angle $Z$ is the right angle, so $XY$ is the hypotenuse. Since $\sin X=\dfrac{4}{7}$ , the side opposite angle $X$ can be represented by $4$ and the hypotenuse by $7$ . Thus let $YZ=4$ and $XY=7$ .

Find the missing leg

Use the Pythagorean theorem:

XZ^2+YZ^2=XY^2.

Substitute $YZ=4$ and $XY=7$ :

XZ^2+4^2=7^2 \Rightarrow XZ^2=33 \Rightarrow XZ=\sqrt{33}.

Compute tangent for angle Y

For angle $Y$ , the opposite side is $XZ=\sqrt{33}$ and the adjacent side is $YZ=4$ . Therefore

\tan Y=\frac{\sqrt{33}}{4}.

Strategy

Hints

Step-by-step Explanation

Study Hints

Strategy

Hints

Step-by-step Explanation