Question

!!! Trigonometry emergency !!!

Answer 1

2.4

Explanation:

tan(theta) is defined as:
`tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}`

in the given diagram we only have the opposite and hypotenuse, but we can use the Pythagorean Theorem to solve for the other two missing sides.

Pythagorean Theorem:
`a^2+b^2=c^2`, where c is the hypotenuse.

Plugging in known values we get the following:

`a^2+12^2=13^2`

in this case the missing side, or the adjacent side is simply "a"

from here we simplify the bases with exponents

`a^2+144=169`

now subtract 144 from both sides

`a^2=25`

take the square root of both sides

`a=5`

So now we know the adjacent side so we can plug it into the tan equation

`tan(z)=(12)/(5)\\\\tan(z)=2.4`