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

Explanation:

Step1: Identify adjacent/hypotenuse

For angle $a$, adjacent side = 27, hypotenuse = 29.

Step2: Use cosine definition

$\cos(a) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{27}{29}$

Step3: Calculate inverse cosine

$a = \cos^{-1}\left(\frac{27}{29}\right)$

Step4: Compute and round

Use calculator to find $\cos^{-1}\left(\frac{27}{29}\right) \approx 21.32^\circ$

Answer:

21.32