Question

find \\(\tan(a)\\) given this triangle. enter your answer as a fraction or as a decimal rounded to three decimal places.
draw
(right triangle with legs 18 and 80, hypotenuse 82, angle at the end of leg 80 is \\(a\\))
show your work here

Explanation:

Step1: Recall tangent definition

For angle $a$, $\tan(a) = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Substitute side lengths

$\tan(a) = \frac{18}{80}$

Step3: Simplify and compute value

$\tan(a) = \frac{9}{40} = 0.225$

Answer:

$0.225$ or $\frac{9}{40}$