Question

Given a triangle with b = 3, c = 9 , and A =21 ° what is the length of a? Round to the nearest tenth

Answer 1

Use the Law of Cosines
a^2 = b^2 + c^2 -2bc *cos(A)
a^2 = 9 +81 -(54 * 0.93358)
a^2 = 90 -50.41332
a^2 = 39.58668
a = 6.2917946565
a = 6.3 (rounded)

Answer 2

Length of a is 6.3

Explanation:

Given: b = 3 , c = 9 and ∠A = 21°

To find: value of a.

We use law of cosines.

The law of cosines is used for calculating one side of a triangle when the angle opposite and the other two sides are known.

a² = b² + c² - 2bc × cos A

a² = 3² + 9² - 2 × 3 × 9 × cos(21)

a² = 9 + 81 - 54 × 0.93

a² = 39.78

a = √39.78

a = 6.307

a = 6.3

Therefore, length of a is 6.3