Question

find the measure of angle a in degrees. round to two decimal places as necessary. draw
21
15
a

Explanation:

Step1: Identify trigonometric ratio

For angle $a$, opposite side = 21, adjacent side = 15. Use tangent: $\tan(a) = \frac{\text{opposite}}{\text{adjacent}}$
<Expression>$\tan(a) = \frac{21}{15}$</Expression>

Step2: Simplify the ratio

Reduce the fraction to simplest form.
<Expression>$\tan(a) = 1.4$</Expression>

Step3: Calculate inverse tangent

Use arctangent to find angle $a$.
<Expression>$a = \arctan(1.4)$</Expression>

Step4: Compute and round the value

Calculate the angle and round to two decimals.
<Expression>$a \approx 54.46^\circ$</Expression>

Answer:

$54.46^\circ$