Question

The diagram below shows the map of a mine.



How deep is the mine shaft?

Answer 1

I know this uses tangent, but I'm not sure whether it's

Answer 2

or 6 tan 20˚

Answer 3

\[\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\]
\[\tan 20°=\frac?6\]

Answer 4

I'm still not sure what it would be. How do you figure it out?

Answer 5

to isolate or solve for ?
multiply both sides of the equation by 6

Answer 6

\[6\times \tan20°=6\times\frac?6\] \(\cdots=\cdots\)

Answer 7

So would it be

Answer 8

I'm new to this stuff, so I'm still confused.

Answer 9

Use this\[a\times\frac ba=\frac{ab}{a}=\frac{\cancel ab}{\cancel a}=\frac b1=b\]

Answer 10

a factor in the numerator and in the denominator may be canceled from the fraction

Answer 11

How do you know whether to use a fraction or not?

Answer 12

a trigonometric function of an angle is always a fraction or ratio of two side-lengths

Answer 13

can you cancel the 6's on the right hand side?

Answer 14

Yes.

Answer 15

and can you simplify the LHS, just remove an implied symbol

Answer 16

6 tan 20˚?

Answer 17

that is it!
\[?=6\tan20°\]