Question

Line AC= 6cm

line AB= 14cm
line BC= 9
find angle A

A. 27
B. 26
C. 30
D. 32

Answer 1

B. 26

Explanation:

You want the measure of angle A in triangle ABC where a=9, b=6, c=14 cm.

Law of Cosines

When three sides of a triangle are given, the angle measures can be found using the law of cosines:

a² = b² +c² -2bc·cos(A)

Solving for angle A, we find ...

A = arccos((b² +c² -a²)/(2bc)

Application

For the given triangle, the angle of interest is ...

A = arccos((6² +14² -9²)/(2·6·14)) = arccos(151/168)

A ≈ 26°

Angle A is ...

B. 26°

<95141404393>