Question

Use the Law of Cosines to find the values of x and y. (PLEASE HELPPP!!!!)

Answer 1

`x = 49.8^\circ\\y = 54.6^\circ`

Explanation:

Kindly refer to the image attached in the answer region for labeling of triangle.

AB = 16

BC = 19

AC = 15

`\angle ABC = x^\circ\\\angle ACB = y^\circ`

We have to find the angles x and y i.e.
`\angle B \text{ and }\angle C`.

Formula for cosine rule:

`cos B = (a^(2)+c^(2)-b^(2))/(2ac)`

Where

a is the side opposite to
`\angle A`,

b is the side opposite to
`\angle B` and

c is the side opposite to
`\angle C`.

`\Rightarrow cos x = (19^(2)+16^(2)-15^(2))/(2 * 19 * 16)\\\Rightarrow cos x = (392)/(608) \\\Rightarrow x = 49.8^\circ`

Similarly, for finding the value of y:

`cos C = (a^(2)+b^(2)-c^(2))/(2ab)\\\Rightarrow cos y = (19^(2)+15^(2)-16^(2))/(2 * 19 * 15)\\\Rightarrow cos y = (330)/(570)\\\Rightarrow y = 54.6^\circ`

Hence, the values are:

`x = 49.8^\circ\\y = 54.6^\circ`