Question

I'm sorry guys, I'm really terrible at trig...

Answer 1

hi there!

The correct answer to this question is 7.51

Explanation:

you would use tangent for this question

tan(43) * 7 equals x

Answer 2

Archimedes is about 7.51 meters from the rock.

Explanation:

They are are looking for the base length of the above right triangle.

The angle whose measurement is given measures 43 degrees.

The side that is opposite of it has it's measurement is given as 7 meters.

We are not looking for the hypotenuse length, but we are looking for the adjacent length.

Recall the following trigonometric right-triangle definitions:

`\sin(\theta)=\frac{\text{opposite side to } \theta}{\text{hypotenuse}}`

`\cos(\theta)=\frac{\text{adjacent side to } \theta}{\text{hypotenuse}}`

`\tan(\theta)=\frac{\text{opposite side to } \theta}{\text{adjacent to}\theta}`

So the things I mentioned that were given or that we wanted to find are the following:

`\theta=43^\circ`

`\text{opposite side to } \theta=7 \text{meters}`

`\text{adjacent side to } \theta=b \text{ meters}`

where
`b` is the number we want to find.

So this means we will need the following above definition to help us solve this problem:

`\tan(\theta)=\frac{\text{opposite side to } \theta}{\text{adjacent to}\theta}`

`\tan(43)=(7)/(b)`

Multiply both sides by
`b`:

`b\cdot \tan(43)=7`

Divide both sides by
`\tan(43)`:

`b=(7)/(\tan(43))`

I'm not inserting right hand side into calculator:

`b=7.5066 \text{ approximately}`

Archimedes is about 7.51 meters from the rock.