Question

1. find the measure of side ad.

Explanation:

Step1: Find AH using tan(22°)

In right triangle AHB, $\tan(22^\circ) = \frac{AH}{HB}$. Given $HB = 12$ m, so $AH = 12 \times \tan(22^\circ)$. $\tan(22^\circ) \approx 0.4040$, so $AH \approx 12 \times 0.4040 = 4.848$ m.

Step2: Find HD using tan(45°)

In right triangle DHB, $\tan(45^\circ) = \frac{HD}{HB}$. Since $\tan(45^\circ) = 1$, $HD = 12 \times 1 = 12$ m.

Step3: Calculate AD

$AD = AH + HD = 4.848 + 12 = 16.848$ m (approx).

Answer:

Approximately $16.85$ m (or more precise value based on $\tan$ calculation)