Answer:
AB = 15
m∠A = 45°
m∠B = 45°
Explanation:
So, to solve for AB, we need to use the Pythagorean theorem.
The Pythagorean theorem tells us, that:
The hypotenuse, in this case AB, is equal to the square root of the sum of the two cathetus squared, or the sides 9 and 12 squared.
Representation in an equation:
Hypotenuse (AB) = √9² + 12².
Now, let's solve for AB:
AB = √9² + 12²
AB = √81 + 144
AB = √225
AB = 15
Let's solve for m∠A:
So, the sum of the angles of every triangle should add up to 180°.
We already know that m∠C = 90°
We can see that m∠A and m∠B angles are exactly the same.
We can see that half of 90° = 45°.
From that, we can infer that m∠A and m∠B measure 45°.
45° + 45° + 90° = 90° + 90°.
90° + 90° = 180°.
The two 45° are m∠A and m∠B, m∠C is 90°. Just to clear any doubts.
So, having all that said, the following answers would be:
AB = 15
m∠A = 45°
m∠B = 45°
Happy to help!