Question

The hypotenuse of right triangle ABC, line segment AC, measures 13 cm. The length of line segment BC is 5 cm.

What is the approximate difference between m∠C and m∠A?

34.8°
44.8°
46.3°
47.9

Answer 1

Since AC is the hypotenuse (13) and BC = 5, the triangle is a 5-12-13 right triangle, so AB = 12.

tan A = opposite/adjacent = BC/AB = 5/12, so A = arctan(5/12) ≈ 22.62°.
Then C = 90° − A ≈ 67.38°.
Difference = C − A = 90° − 2A ≈ 90° − 45.24° = 44.76° ≈ 44.8°.

Answer: 44.8°.