Question

Urgent help needed with right triangle trig!

Answer 1

Let the unknown side's length be 'b' units .

Then by Pythagorean theorem . We have

${b}^{2} = {c}^{2} - {a}^{2}$
Now substituting the values of a and c in the above equation we get the value of b.

${b}^{2} = {24}^{2} - {6}^{2} = 540 \\ \\ b = \sqrt{540} = 6 \sqrt{15}$
We know that ;

$\tan( \theta) = \frac{b}{a} = \frac{6 \sqrt{15} }{6} = \sqrt{15}$