Answer:
- 25°
- x
- 11
- 65°
- x
- 11
Explanation:
You want to know suitable equations that can be solved for x given that AC=x, AB=11, and ∆ABC is a right triangle with angle A=25° and C=90°.
Trig relations
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Angles
The side marked 11 is the hypotenuse, and the side marked x is adjacent to the 25° angle and opposite angle B. We can find the measure of angle B as the complement of angle A:
∠B = 90° -25° = 65°
Application
The cosine relation is ...
cos(A) = AC/AB
cos(25°) = x/11
The sine relation is ...
sin(B) = AC/AB
sin(65°) = x/11
These are equations you can solve to find x.