Question

Solve using the laws of cosine

Answer 1

`\displaystyle 13° = m∠X`

Explanation:

`\displaystyle (x^2 + y^2 - z^2)/(2xy) = cos∠Z \\ (x^2 - y^2 + z^2)/(2xz) = cos∠Y \\ (-x^2 + y^2 + z^2)/(2yz) = cos∠X \\ \\ (-8^2 + 14^2 + 21^2)/(2[14][21]) = cos∠X → (-64 + 196 + 441)/(588) = cos∠X → 0,9744897959... = cos∠X \\ \\ 12,969468847...° = cos^(-1)\:0,9744897959... \\ \\ 13° ≈ 12,969468847...°`

As you can see, the inverse function MUST be used towards the end of your result, or elce you will throw it off!

I am joyous to assist you at any time.

Answer 2

13°

Explanation:

Cosine formula: a² = b² + c² - 2(b)(c)cos(a)

8² = 21² + 14² - 2(21)(14)cos(x)

64 = 441 + 196 - 588cos(x)

Bring constants to one side

64 = 441 + 196 - 588cos(x)

-441 -441 -196

-196

-573 = -588cos(x)

Divide by the coefficient

-573/-588 = -588cos(x)/-588

cos(x) = 573/588

To find x you need to use arcsin or cos^-1

x = arccos(573/588) = 12.969°