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.

Explanation:

Step1: Identify trigonometric ratio

In right - triangle \(ABC\), we know the hypotenuse \(AB = 130\) in and angle \(A=47^{\circ}\), and we want to find the adjacent side \(b\) to angle \(A\). We use the cosine function: \(\cos(A)=\frac{\text{adjacent}}{\text{hypotenuse}}\), so \(\cos(A)=\frac{b}{AB}\).

Step2: Solve for \(b\)

We can rewrite the formula as \(b = AB\times\cos(A)\). Substitute \(AB = 130\) and \(A = 47^{\circ}\). We know that \(\cos(47^{\circ})\approx0.681998\). Then \(b=130\times\cos(47^{\circ})\).

Step3: Calculate the value

\(b = 130\times0.681998=88.65974\).

Step4: Round the answer

Rounding \(88.65974\) to the nearest whole number, we get \(b\approx89\).

Answer:

89