Given a triangle ABC such that AB = 4. AC = squareroot (41) and BC = 5.

Find the measures of the interior angles of ABC.

A = 51.3°, B = 90°, C = 38.7°

Step-by-step explanation:

The given lengths satisfy the Pythagorean theorem:

(√41) ² = 4² + 5² ⇒ 41 = 16 + 25

so we know the triangle is a right triangle. The right angle is opposite the longest side, so is angle B, opposite side AC.

The remaining angles can be found using trig functions. For example, we know ...

tan (A) = BC/AB = 5/4

A = arctan (5/4) ≈ 51.3°

Then the other acute angle is ...

C = 90° - 51.3° = 38.7°

Angles A, B, C are ...

(A, B, C) = (51.3°, 90°, 38.7°)