In a right triangle, the sine of an angle compares the side across from that angle with the hypotenuse, the side across from the right angle. When a figure labels all three sides and asks for the sine of a named angle, identify those two sides before writing the fraction. The tempting slip is to use the leg touching the named angle instead of the one across from it.
Hints
- Hint 1
The hypotenuse is the side across from the marked right angle, and it goes on the bottom of a sine ratio. Which labeled side lies across from the square at ?
- Hint 2
The opposite side is the one across from the angle you’re using. For angle , look for the leg that doesn’t touch . Which length is written on that leg?
Step-by-step
Read the sine ratio from the triangle
Step 1Find the hypotenuse
No Desmos needed. The labeled sides give the exact sine ratio. The square marks a right angle at , so is across from it. That makes the hypotenuse, the side across from the right angle.
- Step 2
Find the side opposite angle J
From , the side is across the triangle and doesn’t touch , so it is the opposite side. touches , so it isn’t opposite. Choose the opposite side from the angle the question names.
- Step 3
Write the sine ratio
By definition, sine is opposite over hypotenuse. Use the two sides you found:
The value of is . Choice A.