Question

Given: triangle ABC, AB = 5√2, measure angle A = 45 degrees, measure angle C = 30 degrees. Find BC and CA.

Answer 1

To find BC and CA in triangle ABC, we can use the Law of Sines which states that for any triangle ABC, the ratio of each side length to the sine of its opposite angle is constant.

Step-by-step explanation:

To find BC and CA in triangle ABC, we can use the Law of Sines. The Law of Sines states that for any triangle ABC, the ratio of each side length to the sine of its opposite angle is constant. In this case, we have:
BC / sin(A) = AB / sin(C) and CA / sin(B) = AB / sin(C)
Plugging in the given values:
BC / sin(45) = 5√2 / sin(30)
CA / sin(135) = 5√2 / sin(30)
Simplifying, we have:
BC ≈ 5 and CA ≈ 5√2