Question

Find the value of x and y please

Answer 1

`x = 7( √(2) + √(6) ) \\ y = 14 √(3)`

Answer 2

The answer to your question is x =
`7√(2)` and y =
`14√(3)`

Explanation:

To find x and y use trigonometric functions

- Find x

To find x use the trigonometric function cosine

cosine Ф = adjacent side/hypotenuse

- Solve for adjacent side (x)

x = hypotenuse x cos Ф

- Substitution

x = 14
`√(2)` cos 60

Simplification

x = 14
`√(2)` (0.5)

x = 7
`√(2)`

- Find y

-Find the length of the opposite side of the small triangle

Opposite side = sine Ф x hypotenuse

Opposite side = 14
`√(2)` x sin 60

Opposte side = 14
`√(2)` (
`√(3)`/2)

Opposite side = 7
`√(6)`

- Find the length of y

y = Opposite side/sin Ф

y =
`7√(6)` /
`√(2) /2`

y = 14
`√(3)`