A right triangle has sides 5.0 m,12 m,and 13 m.The largest angle not 90° of this triangle is nearest:
A) 21°.
B) 23°.
C) 67°.
D) Not attainable since this is not a right triangle.

Question

Quizplus · Accepted Answer

In a right triangle, the largest angle must be 90°, so this is not a right triangle. Therefore, we can use the Law of Cosines to determine the largest angle.

cos C = (a^2 + b^2 - c^2) / 2ab

where a, b, and c are the side lengths and C is the angle opposite side c (the largest angle).

Plugging in the values gives:

cos C = (5^2 + 12^2 - 13^2) / 2(5)(12) 
cos C = 0.6417 
C = cos^-1 (0.6417) 
C ≈ 50.1°

Therefore, the nearest choice is C, 67°.

A Right Triangle Has Sides 5