Question

What is x? how would i find the value of x?

Answer 1

In this problem, we want to find the missing side of a right triangle.

Since we have been given one side and an angle, we will need to use a trigonometric function. The general functions for this type of triangle are

- sine

- cosine

- tangent

Each one depends on which side is given and which side you're trying to find.

We have the diagram

The arrow always points to the opposite side, which means we know the adjacent side is 13.

Since we are given the adjacent side and want to find the opposite side, we need to use the tangent function:

`\tan\theta=\frac{\text{ opposite}}{\text{ adjacent}}`

Since the angle is 73 degrees, we set up the ratio like this:

`\tan73^(\circ)=(x)/(13)`

We should multiply by 13 on both sides to isolate the variable, x:

`\begin{gathered} 13\cdot\tan73^(\circ)=(x)/(13)\cdot13 \\ \\ 13\tan73^(\circ)=x \end{gathered}`

Before we put this in the calculator, ensure that your calculator is set to degrees. You can do this by pushing the "mode" button. Select the option that says "degree."

Let's finish this off by keying in the expression directly into the calculator:

`x=13\cdot\tan(73)\approx43`

Although the calculator will read about 42.52108....., we need to round to the nearest whole number.

`\boxed{x\approx43}`