Question 87·Easy·Geometry and Trigonometry

0 / 200

In right triangle $JKL$ shown, the lengths of the sides are labeled in the figure.

Which choice gives the value of $\sin J$ ?

For right-triangle trig questions, first find the hypotenuse by locating the side opposite the right angle. Then, for the requested angle, identify the opposite side (across from the angle) and plug into the correct ratio: $\sin=\dfrac{\text{opposite}}{\text{hypotenuse}}$ , $\cos=\dfrac{\text{adjacent}}{\text{hypotenuse}}$ , $\tan=\dfrac{\text{opposite}}{\text{adjacent}}$ .

Hints

Click me!

Start with the definition of sine

Use $\sin(\text{angle})=\dfrac{\text{opposite}}{\text{hypotenuse}}$ .

Find the hypotenuse from the right angle

The hypotenuse is the side opposite the right angle (the $90^\circ$ angle).

Locate the opposite side

For $\sin J$ , find the side directly across from vertex $J$ in the figure.

Desmos Guide

Compute candidate ratios

In Desmos, enter the expressions 5/13 and 12/13 to see their decimal values.

Match the numerator to the opposite side

Use the figure to decide whether the side opposite $\angle J$ is the leg labeled 5 or the leg labeled 12.

Choose the matching option

Select the answer choice that equals $\dfrac{\text{(opposite side length)}}{13}$ , since 13 is the hypotenuse.

Step-by-step Explanation

Identify the opposite side and hypotenuse

Because $\angle K$ is a right angle, the side opposite it, $\overline{JL}$ , is the hypotenuse, so $JL=13$ . For $\angle J$ , the side across from $J$ is $\overline{KL}$ , so $KL=5$ .

Use the sine ratio

\sin J=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{KL}{JL}=\frac{5}{13}

So the correct choice is $\dfrac{5}{13}$ .

Question 87·Easy·Geometry and Trigonometry

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation