Question

Find the value of the variable leave answer in simplest radical form

Answer 1

X is 7 and y is 7 square root of 3.

Answer 2

Answer:

x = 7 and y = 7√3

Step-by-step explanation:

Let's review, and then apply, the definition of "cosine."

cos Ф = adjacent side / hypotenuse.

Here, x is the adjacent side, Ф is the angle and is 60°, and 14 represents the length of the hypotenuse.  cos Ф = adjacent side / hypotenuse becomes:

adjacent side = hypotenuse * cos Ф.

Here, Ф = 60° and cos Ф = cos 60° = 1/2.  Therefore,

in this case, x = 14(1/2), or 7.

Applying the definition of sine:

sin Ф = opp / hyp.  In this case, sin Ф = sin 60° = y/14, so that

y = 14 sin 60°, or y = 14(√3 / 2) = 7√3.

In summary, x = 7 and y = 7√3.