Question

When given all three side lengths of a triangle but none of the angle measures, you can solve for all angle measures using __________.

A. The law of sines
B. The alternative form of the law of sines
C. The alternative form of the law of cosines
D. The Pythagorean Theorem

Answer 1

Answer;

C. The alternative form of the law of cosines

When given all three side lengths of a triangle but none of the angle measures, you can solve for all angle measures using the alternative form of the law of cosines.

Explanation;

• From the law of cosines, given that a, b and c are the edges of a triangle and A, B and C are the corresponding interior angles of the the triangle.

Then; a² = b² + c² − 2 bc cos A, or

b² = a² + c² − 2 bc cos B, or

c² = a² +b ² − 2 bc cos C

Therefore; when given all the sides or edges of the triangle;

• we can use the law of cosines to find one angle, then
• we use the law of cosines again to find the second angle, and finally,
• we use the point that angles in a triangle add up to 180 to get the third angle;