Question

Use a special right triangle to find the value of y. Write as a decimal rounded to the nearest 10th

Answer 1

Given:

The figure of a right angle triangle.

To find:

The value of y.

Solution:

in a right angle triangle,

$\sin \theta=\dfrac{Opposite}{Hypotenuse}$

In the given right triangle,

$\sin 60^\circ=\dfrac{6}{y}$

$\dfrac{\sqrt{3}}{2}=\dfrac{6}{y}$

On cross multiplication, we get

$\sqrt{3}y=12$

$y=\dfrac{12}{\sqrt{3}}$

$y=\dfrac{12\sqrt{3}}{3}$

$y=4\sqrt{3}$

Therefore, the value of y is $4\sqrt{3}$ units.