A trigonometric ratio compares sides relative to a chosen angle. If a right triangle gives the sine of one acute angle but asks for the tangent of the other acute angle, label the sides from the given sine ratio, then find the missing leg. A familiar right-triangle triple can save arithmetic. The trap is keeping the side labels fixed when you switch angles.
Hints
- Hint 1
The hypotenuse is across from the right angle, so it is . Sine means opposite over hypotenuse. From angle , which leg belongs on top of the given sine ratio?
- Hint 2
The -- triple has legs in the ratio and a hypotenuse in the ratio . The sine ratio identifies one leg and the hypotenuse. Which leg gets the position?
- Hint 3
Tangent means opposite over adjacent. The adjacent leg touches your angle but isn't the hypotenuse. Look from , not : which of and belongs on top?
Step-by-step
Use the side ratio and switch angles
Step 1Label the sides in the sine ratio
No Desmos needed. The -- right-triangle triple gives the missing side ratio exactly. The hypotenuse is across from the right angle at , so it's . Sine means opposite over hypotenuse, and is opposite , so:
- Step 2
Find the missing leg's position
In the -- right-triangle triple, and are the legs and is the hypotenuse. has the position and has the position, so the remaining leg has the position: . These are side ratios, not necessarily the triangle's actual lengths.
- Step 3
Write tangent from angle B
Switching from to swaps which leg is opposite and which is adjacent. Tangent means opposite over adjacent. From angle , is opposite and is adjacent, so: . The value of is . Choice B.