A sine ratio in a right triangle compares the leg across from the named angle with the hypotenuse, across from the right angle. If that hypotenuse isn't labeled, a familiar right-triangle triple may give it immediately. Don't substitute the leg touching the named angle: that leg belongs in cosine, the adjacent-over-hypotenuse ratio.
Hints
- Hint 1
The hypotenuse is always across from the right angle, even if the figure isn't drawn to scale. Find the little square at . Which side lies across from it?
- Hint 2
The legs of lengths and form a familiar right-triangle triple: --. The hypotenuse is its longest side, so what length does that give the unlabeled side?
- Hint 3
The opposite side lies across from the angle you're using, not across from the right angle. Stand at angle : which leg lies across from it rather than touching it?
Step-by-step
Find the hypotenuse, then use sine
Step 1Identify the hypotenuse
No Desmos needed. The given legs fit a familiar right-triangle triple. The square at marks the right angle, so , across from , is the hypotenuse, the longest side.
- Step 2
Find the unlabeled side
The legs and fit the -- right-triangle triple, so the hypotenuse has length .
- Step 3
Find the side opposite the named angle
From at , lies across the triangle, so it's the opposite side. Choose opposite relative to the named angle, not the right angle. The leg touches , so it's adjacent instead.
- Step 4
Write the sine ratio
The sine ratio is opposite over hypotenuse. For angle , that gives . Choice A.