Question

Calculate the value of A to one decimal place

Answer 1

Okay, you will need to use the law of cosines for this problem.

The Law of Cosines states (in this case): a^2 = b^2 + c^2 - 2 * b * c * cos A, where "a" is the side opposite angle A (7 inches), and b and c are the other two sides.

Plug the numbers in and you get: 7^2 = 5^2 + 9^2 - 2 * 5 * 9 * cos A, or:

49 = 25 + 81 - 90 * cos A.

Subtract (25 + 81) from both sides to get:

-57 = -90 * cos A.

Divide by -90 on both sides:

cos A = 19/30

To find A, you do the inverse trigonometric function to get:

cos^-1 of (19/30) = A.

I don't have a calculator that can do this right now, but if you plug the left side of the above equation into it (make sure it is in degrees, not radians), you should get A.

Answer 2

Value of A is 50.7°

Explanation:

Given: All sides of triangle.

let, a = 7 in. , b = 5 in. and c = 9 in.

We have to find Value of A that is measure of Angle A.

Figure is attached.

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

⇒ 7² = 5² + 9² - 2 × 5 × 9 × cos A

49 = 25 + 81 - 90 × cos A

49 - 106 = -90 × cos A

-57 = -90 × cos A

cos A =
`(57)/(90)`

A =
`cos^(-1)\,0.63`

A = 50.7°

Therefore, Value of A is 50.7°