Question

In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A.

Answer 1

38 degrees

Explanation:

The other answer is very wrong i just took the lesson it was in!!

Answer 2

This case, where you have 3 given sides and no given angles, requires the use of the cosine law. The cosine law is as follows:


`a^(2) = b^(2) + c^(2) - 2bc\:cosA`

Add your given values to the equation and simplify:

`3^(2) = 5^(2) + 7^(2) -2(5)(7)cosA`

`9 = 25 + 49 - 70cosA`

`9 - 25 - 49 = -70cosA`

`-65 = -70cosA`

`cosA = (-65)/(-70)`

`cosA = (13)/(14)`

`A = cos^(-1)\:(13)/(14)`

Use your scientific calculator to evaluate. Round the answer to as many decimal places as the question asks:


`A = 21.7867893...\:^(\circ)`

Hope this helped :)