Question

How do you solve `tan theta = 5/9`?

Answer 1

`theta = 37.9°`

Explanation:

The process involved here is one called finding "arctan".

If you are given the measure of an angle, you can use a calculator or tables to find any trig ratio of any angle.

For example: `Sin20° = 0.342," "cos 58° =0.530," "tan 67°=2.356`

If you know the ratio, but need to find the angle, this is the 'arc-ratio'

(It is shown as `sin^-1` and is not to be confused with `1/(sin theta)`

You will have to use tables or a calculator to find the angle.

Using tables:
Step 1. Find the answer as a decimal: `tan theta = 7/9 = 0.778`
Step 2. Using a table of tan values, look for `0.778`
Step 3. Read off the angle. `theta = 37.9°`

Using a calculator: - remember they work differently.

D.A.L. : Key in: `color(blue)("shift "tan^-1 (7/9) =)`

or: D.A.L.: `color(blue)(7div9 = " shift" tan^-1 ANS =)`

or: `" "color(blue)(7div 9 = " shift" tan^-1)" "larr` usually older calculators

The display will give you the angle as `37.87498...`

Angles are usually given to 1 decimal place.

`theta = 37.9°`

[D.A.L. means direct algebraic logic]