Question

Find the measures of angle A and B. Round to the nearest degree.

Answer 1

32.2

Explanation:

Answer 2

• A ≈ 32°
• B ≈ 58°

Explanation:

You want the measures of angles A and B in right triangle ABC with hypotenuse AB = 15, and side BC = 8.

Trig relations

The mnemonic SOH CAH TOA reminds you of the relationships between side lengths and trig functions in a right triangle:

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Application

Here, the hypotenuse is given as AB=15. The side opposite angle A is given as BC=8, so we have ...

sin(A) = 8/15 ⇒ A = arcsin(8/15) ≈ 32°

The side adjacent to angle B is given, so we have ...

cos(B) = 8/15 ⇒ B = arccos(8/15) ≈ 58°

Of course, angles A and B are complementary, so we can find the other after we know one of them.

B = 90° -A = 90° -32° = 58°

The measures of the angles are A = 32°, B = 58°.

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Additional comment

The inverse trig functions can also be called arcsine, arccosine, arctangent, and so on. On a calculator these inverse functions are indicated by a "-1" exponent on the function name—the conventional way an inverse function is indicated when suitable fonts are available.

You will note the calculator is set to DEG mode so the angles are given in degrees.