Question

find the measure of the side of the right triangle whose length is designated by a lowercase letter.
a ≈ □ cm
(round to the nearest whole number as needed.)

Explanation:

Step1: Identify trigonometric ratio

For $\angle A = 39^\circ$, side $a$ is opposite, side $b=150$ cm is adjacent. Use tangent:
$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Step2: Substitute known values

$\tan(39^\circ) = \frac{a}{150}$

Step3: Solve for $a$

Rearrange to isolate $a$:
$a = 150 \times \tan(39^\circ)$
Calculate $\tan(39^\circ) \approx 0.8098$, so:
$a \approx 150 \times 0.8098$

Step4: Compute final value

$a \approx 121.47$

Answer:

$a \approx 121$ cm