Question

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

Answer 1

Answer:

38 degrees

Step-by-step 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:
$3^{2} = 5^{2} + 7^{2} -2(5)(7)cosA$
$9 = 25 + 49 - 70cosA$
$9 - 25 - 49 = -70cosA$
$-65 = -70cosA$
$cosA = \frac{-65}{-70}$
$cosA = \frac{13}{14}$
$A = cos^{-1}\:\frac{13}{14}$

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 :)