Problem 24 of 7
Derive Law of Cosines for right triangle with angle A = 90 degrees.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
construct altitude and simplify.
Hidden until you reveal it.
Construct altitude and simplify using distance/Pythagorean decomposition.
Enter your answer
Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Drop an altitude or place triangle on coordinate axes.
2. Express projected components using cosine and sine.
3. Apply Pythagorean theorem and simplify with sin^2+cos^2=1.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Proof that assumes right triangle only for all cases.