Question

find the missing side length. round to the nearest tenth
image of a right triangle with a 62° angle, one leg labeled 7 m, and the other leg labeled y
y=

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled, and we know one angle (\(62^{\circ}\)) and the adjacent side to this angle (length \(7\) m), and we need to find the opposite side \(y\). The tangent function is defined as \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\). So \(\tan(62^{\circ})=\frac{y}{7}\).

Step2: Solve for y

Multiply both sides of the equation \(\tan(62^{\circ})=\frac{y}{7}\) by \(7\) to get \(y = 7\times\tan(62^{\circ})\). We know that \(\tan(62^{\circ})\approx1.8807\). Then \(y=7\times1.8807 = 13.1649\).

Step3: Round to nearest tenth

Rounding \(13.1649\) to the nearest tenth, we look at the hundredth place digit which is \(6\). Since \(6\gt5\), we round up the tenth place digit. So \(13.1649\approx13.2\).

Answer:

\(13.2\)