Question

find the measure of side c.
a = 35 m
c = m (round the answer to the nearest whole number.)

Explanation:

Step1: Identify the trigonometric relation

In right - triangle \(ABC\) with right - angle at \(C\), we know the side \(a = 35\) m and angle \(A=41^{\circ}\), and we want to find the hypotenuse \(c\). We use the sine function since \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin A=\frac{a}{c}\).

Step2: Rearrange the formula to solve for \(c\)

From \(\sin A=\frac{a}{c}\), we can rewrite it as \(c=\frac{a}{\sin A}\).

Step3: Substitute the values

We know that \(a = 35\) m and \(A = 41^{\circ}\), and \(\sin41^{\circ}\approx0.656\). So \(c=\frac{35}{\sin41^{\circ}}=\frac{35}{0.656}\approx53.35\).

Step4: Round the result

Rounding \(53.35\) to the nearest whole number gives \(53\).

Answer:

\(53\)