In a right triangle, cosine compares the leg next to the chosen angle with the hypotenuse, the side across from the right angle. Find the hypotenuse first, then identify the leg beside the marked angle. The tempting traps are using the leg across from the angle or turning the fraction upside down.
Hints
- Hint 1
The hypotenuse is always across from the right-angle marker, even though it also touches the marked acute angle. Which labeled side lies across from the right angle where the wall meets the ground?
- Hint 2
The adjacent leg touches but isn't the hypotenuse. At the bottom of the ramp, is that the horizontal ground segment or the vertical wall? Cosine uses adjacent over hypotenuse.
Step-by-step
Identify the sides in the cosine ratio
Step 1Find the hypotenuse
No Desmos needed. Both sides of the cosine ratio are labeled. The hypotenuse is across from the right angle. The wall and ground meet at that angle, so the 13-foot ramp is the hypotenuse.
- Step 2
Find the leg next to the angle
At , the 12-foot ground segment touches the angle. It's the adjacent leg: the side beside the angle that isn't the hypotenuse. The wall is across from , so it isn't the leg cosine uses.
- Step 3
Write the cosine ratio
means the cosine of , so use adjacent over hypotenuse:
The cosine of the angle the ramp makes with the ground is . Choice B.