Question

How do I solve for 15? It says to use tan30=20/a

Answer 1

Since we have a right triangle, we can relate the given angle and the legs a and 20 by means of the tangent function ,that is,

`\tan 30=(20)/(a)`

Since tangent of 30 degrees is

`\text{tan}30=\frac{\text{ opposite side to angle 30}}{\text{ adjacent side to angle 30}}=\frac{1}{\sqrt[]{3}}`

we have that

`\frac{1}{\sqrt[]{3}}=(20)/(a)`

Then, by cross multiplying the numbers, we have

`1* a=20*\sqrt[]{3}`

Therefore, we have:

`a=20\sqrt[]{3}=34.64`

By rounding to the nearest whole number, the answer is: 35 units