Solve ABC where ∠C = 90°, a = 15 cm, and b = 7 cm.

c ≈ 16.55cm ; ∠A = 65 degrees ; ∠B = 25 degrees

Step-by-step explanation:

Because of the Pythagorean theorem, we can solve for c.

This theorem states: a^2 + b^2 = c^2

Since there can only be 180 degrees in a triangle, angle C must be our largest angle. This means that side c is our hypotenuse (the longest side).

Using all of this information, we can say that 15^2 + 7^2 = c^2.

Simplifying that equation, we get that 274 = c^2.

In order to find c, we must square root both sides, and we find that c is about 16.55 cm long.

Using SOHCAHTOA, we know that the tan(∠B)=. Therefore, the arctan () = ∠B.

Once you find that ∠B is about 25 degrees, you can add ∠B and ∠C together and subtract that from 180 to find ∠A.

∠A = 65 degrees.