We can start solving this problem by using the following property of the cosine of a sum:
Now, let's notice that the trigonometric relations are obtained by comparing the sides of a right triangle. So, we have:
So, we can find the missing sides a and b, and then use them to calculate sin A, cos B, and sin B.
53² = a² + 28²
a = √(53³-28²)
a = √(2025)
a = 45
and
b² = 24² + 7²
b = √(24² + 7²)
b = √(625)
b = 25
So, we have:
• sin A = a/53 = 45/53
,
• sin B = 7/b = 7/25
,
• cos B = 24/b = 24/25
Now, we can use those values to find: