Question

Solve for x and y. 30-60-90 triangles

Answer 1

Answer:

• $x = 3$

• $y=3\sqrt{3}$

Step-by-step explanation:

From the given right-angle triangle

The angle = ∠60°

• The adjacent to the angle ∠60° is x.

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

The hypotenuse = 6

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = x and hypotenuse = 6

cos 60° = x / 6

6 × cos 60° = x

x = 3

Thus, the value of x is:

• x = 3

And using the trigonometric ratio

sin 60° = opposite / hypotenuse

substituting opposite = y and hypotenuse = 6

$sin\:60^{\circ }\:=\:\frac{y}{6}\:$

$y=6\:\times\:sin\:60^{\circ }$

   $=6\times \frac{\sqrt{3}}{2}$                   ∵ $\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}$

   $=3\sqrt{3}$

Therefore, the value of y is:

• $y=3\sqrt{3}$

Summary:

• $x = 3$

• $y=3\sqrt{3}$