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: Use tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 38^{\circ}$, the adjacent side to $\theta$ is $b = 230$ cm and the opposite side is $a$. So, $\tan38^{\circ}=\frac{a}{b}$.

Step2: Solve for $a$

Since $b = 230$ cm and $\tan38^{\circ}\approx0.7813$, we can rewrite the equation as $a=b\times\tan38^{\circ}$. Substitute $b = 230$ into the equation: $a = 230\times0.7813$.

Step3: Calculate the value of $a$

$a=230\times0.7813 = 179.699$ cm.

Step4: Round to the nearest whole number

Rounding $179.699$ to the nearest whole number gives $a\approx180$ cm.

Answer:

$180$