# How do I solve this problem using trigonometry?

Mar 29, 2018

You have to use trigonometry

#### Explanation:

First, find label the side. Opposite is the side opposite of the angle, adjacent is the side next to the angle and the hypotenuse is the longest side.

Then, depending on the information you have (in this case you have the opposite and the hypotenuse) you will use the ratio for either $\tan$, $\sin$ or $\cos$ (in this case you have sin, which is opposite side divided by the hypotenuse).

So when you fill your information into the ratio you should have $\frac{5}{y} = \sin \left(150\right)$

Once you reverse the equation you would therefore be multiplying $5 x \sin \left(150\right)$ to get $y$.
$S \in$ is a function on your calculator so make sure to type it in there.

Mar 29, 2018

$x = 5 \sqrt{3}$

$y = 10$

#### Explanation:

.

In the right triangle, the angle next to the ${150}^{\circ}$ angle is:

$180 - 150 = {30}^{\circ}$

This make this triangle a special right triangle which is called a ${30}^{\circ} , {60}^{\circ} , {90}^{\circ}$ triangle.

In such a triangle, the side opposite the ${30}^{\circ}$ angle is half the hypotenuse. As such,

$y = 2 \left(5\right) = 10$

And the side adjacent to the ${30}^{\circ}$ angle is equal to $\sqrt{3}$ times the opposite side.

$x = 5 \sqrt{3}$

You can also use the Pythagoras' formula ${c}^{2} = {a}^{2} + {b}^{2}$ to solve for the third side. The third way to solve it is using trigonometry.

Mar 29, 2018

$x = 8.66 \mathmr{and} y = 10$

#### Explanation:

The angle of 150° is the exterior angle of the triangle. Its supplement is 30°, which gives us an angle in the triangle.

Using 30°  as the reference angle, $x$ is the adjacent side, $5$ is the opposite side and $y$ is the hypotenuse,

tan 30° = 5/x" "(larr"opposite")/(larr"adjacent")

x= 5/(tan30°)

$x = 8.66$

sin 30° = 5/y" "(larr"opposite")/(larr"hypotenuse")

y = 5/(sin30°)

$y = 10$