How do I find the missing angle?

Question

How do I find the missing angle using trig?

Answer 1

You should use the law of cosines, namely that c² = a² + b² - 2ab cos(2θ),

with a = 10, b = 17, and c = 24, so in general we have:

2ab cos(2θ) + c² = a² + b² ----> 2ab cos(θ) = a² + b² - c² ------->

cos(θ) = (a² + b² - c²) / (2ab) -----> θ = arccos[ (a² + b² - c²) / (2ab) ].

Finally, if you need θ in degrees, then you need to multiply the answer you get by 180 degrees / π.

Answer 2

The central concept this question is targeting is the law of cosines: https://mathworld.wolfram.com/LawofCosines.html

Once you understand the law of cosines, the answer should be clear.