Question

Find the values of x and y. Pls helpI’m helpless at math

Answer 1

• x = 1

• 
  `y=(√(3))/(2)`

Explanation:

From the given right-angle triangle

The angle = ∠60°

• The adjacent to the angle ∠60° is 1/2.

• The opposite to the angle ∠60° is y.

The hypotenuse = x

Determining the value of x:

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = 1/2 and hypotenuse = x

`cos\:60^(\circ )=\:\:((1)/(2))/(x)`

`\cos \left(60^(\circ \:)\right)=(1)/(2x)`

`(1)/(2)=(1)/(2x)` ∵ cos (60°) = 1/2

`2x=2`

Dividing both sides by 2

`(2x)/(2)=(2)/(2)`

Simplify

`x=1`

Thus, the value of hypotenuse x is:

x = 1

Determining the value of y:

Using the trigonometric ratio

sin 60° = opposite / hypotenuse

As we have already determined the value of hypotenuse x = 1

substituting opposite = y and hypotenuse = 1

sin 60° = y/1

y = 1 × sin 60°

`y=(√(3))/(2)` ∵
`\sin \left(60^(\circ \:)\right)=(√(3))/(2)`

Therefore, the value of y is:

`y=(√(3))/(2)`

Summary:

• x = 1

• 
  `y=(√(3))/(2)`