In triangle ABC, a = 8, b = 6, and C = 60°. find the measure of A.

Solution:

Given, a = 8, b = 6 and angle C = 60°

We have to find the measure of angle A.

Using cosine formula,

cos C = (a² + b² - c²)/2ab

cos 60° = [(8)² + (6)² - c²]/[2(8)(6)]

1/2 = [64 + 36 - c²]/(96)

1/2 = (100 - c²)/96

On simplification,

100 - c² = 48

c² = 100 - 48

c² = 52

On taking square root,

c = 2√13

Similarly, cos A = (b² + c² - a²)/2bc

cos A = [(6)² + (2√13)² - (8)²)/[2(6)(2√13)]

cos A = (36 + 52 - 64)/24√13

cos A = 24/24√13

cos A = 1/√13

Taking inverse,

A = cos^-1(1/√13)

A = 74°

Therefore, the measure of A is 74°.

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In triangle ABC, a = 8, b = 6, and C = 60°. find the measure of A.

Summary:

In triangle ABC, a = 8, b = 6, and C = 60°. The measure of A is 74°.