Question

ABC is an obtuse triangle. Given that CB = 20, the measure of A = 30°, and the measure of B = 45°, which of the expressions listed would be used to find how long CA is? (Note: For ABC, where a, b, and c are the lengths of the sides opposite A, B, and C, respectively, SinA/a=SinB/b=SinC/c.)
1. 45sin20/sin30
2. 20sin30/sin45
3. 20sin45/sin30
4. sin45/20sin30

Answer 1

Answer:

option 3

Step-by-step explanation:

Using the Sine rule in Δ ABC, that is

$\frac{a}{sinA}$ = $\frac{b}{sinB}$, that is

$\frac{20}{sin30}$ = $\frac{CA}{sin45}$ ( cross- multiply )

CA × sin30° = 20 × sin45° ( divide both sides by sin30° )

CA = $\frac{20sin45}{sin30}$ → (3)