Question

find the measure of the side of the right triangle whose length is designated by a lowercase letter b. round answers to the nearest whole number.
b ≈ 103 in (do not round until the final answer. then round to the nearest whole number.)

Explanation:

Step1: Identify the trigonometric ratio

We know the hypotenuse $AB = 168$ in and we want to find the adjacent - side $b$ to the angle $A=38^{\circ}$. We use the cosine function, $\cos(A)=\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos(A)=\frac{b}{AB}$

Step2: Substitute the values

Substitute $A = 38^{\circ}$ and $AB = 168$ into the formula. $\cos(38^{\circ})=\frac{b}{168}$.
$b = 168\times\cos(38^{\circ})$

Step3: Calculate the value of $b$

We know that $\cos(38^{\circ})\approx0.7880$. Then $b = 168\times0.7880=132.384$.

Step4: Round the answer

Round $132.384$ to the nearest whole number. $b\approx132$ in.

Answer:

$132$ in