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

Find the values of x and y. Pls helpI’m helpless at math-example-1

1 Answer

4 votes

Answer:

  • 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)
User Larney
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