Question

a right triangle has side lengths that are consecutive intergers and a perimeter of 12 feet. what are the angles of the triangle? A 30,60, and 90. B 33.47, 56.53, and 90. C 36.87, 53.13, and 90. D 40.16, 49.84, and 90.

Answer 1

Answer: C) 36.87, 53.13, 90

Step-by-step explanation:
Perimeter: P=a+b+c
12=3+4+5

Use the Law of Cosine to find the angles.
cos(A)=(b^2+c^2-a^2)/2bc
=(4^2+5^2-3^2)/2(4)(5)=32/40
cos^-1(32/40)=36.87
A=36.87

cos(B)=(a^2+c^2-b^2)/2bc
=(3^2+5^2-4^2)/2(3)(5)=18/30
cos^-1(18/30)=53.13
B=53.13

C=180-A-B
=180-36.87-53.13=90
C=90