Question

I am just started doing trigonometry and I am already lost. Help?

6. Find the value of x. Round to the nearest tenth. (see photo)

8. Find the value of x. Round to the nearest tenth. (photo)

11. Find the value of x. Round to the nearest degree. (photo)

13. Find the value of x. Round to the nearest degree. (photo)

14. Find the value of x to the nearest degree. (photo)

Answer 1

SOH CAH TOA

Explanation:

Finding sides (first 2 pictures)

For finding sides of a triangle, you first must "map" the triangle using the given angle as a reference. In this case (for the first picture) use the angle with the measure of 32. The side directly across from the reference angle is the opposite. Label it "O." The side directly across from the right angle is the hypotenuse. Label it "H." Thus, the other side (12) must be the adjacent side. Label it "A." Since you are given
`x` and
`12`, and you know that
`x` is the hypotenuse and
`12` is the adjacent side, you use the CAH operation, meaning
`\cos = \frac{\text{adjacent}}{\text{hypotenuse}}`.

Set it up like so:

`\cos(32) = (12)/(x)`

Use order of operations:

`x = (12)/(\cos(36))`

Plug that in your calculator and that's your answer.

Finding angles (last 3 pictures)

In the third picture, you are given two sides and x. When finding angles, you only use what you are given. However, instead of using sin, cos, tan, you must use the inverse, which is
`\sin^(-1)` and so on.

Since you are trying to find x, you still use it as your reference angle. 20 is the hypotenuse and 11 is adjacent. Don't worry about the other side- it's not necessary unless it's given. Since you are given the hypotenuse and the adjacent, you use the
`\cos` property. (inverse)

It's done like so:

`\cos^(-1)(x) = (11)/(20) \\\\x = \cos^(-1)((11)/(20))`

Put that in your calculator, and that's the answer! The rest of the angle problems are done the same way, just using different sides.