Question

Solve the triangle.

С
a
b
a =5, b=3, c=4
А
B
C
A-°
(Type your answer in degrees. Round to one decimal place as needed.)

Answer 1

A = 90°

B = 37°

C = 53°

Explanation:

Given three sides of a triangle, the Law of Cosines can be used to find the angles.

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For angle A (the largest), we can use ...

a² = b² +c² -2bc·cos(A)

Solving for A, we get ...

A = arccos((b² +c² -a²)/(2bc)) = arccos((3² +4² -5²)/(2·3·4)) = arccos(0)

A = 90°

We can use a similar equation for angle B:

B = arccos((a² +c² -b²)/(2ac)) = arccos((25 +16 -9)/(2·5.4)) = arccos(4/5)

B ≈ 37°

The sum of angles is 180°, so ...

C = 180° -90° -37°

C = 53°