Question

find m∠c.

write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠c = °
submit

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(ABC\) (right - angled at \(B\)), to find \(\angle C\), we can use the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. For \(\angle C\), the opposite side is \(AB = 3\) and the adjacent side is \(BC=6\). So, \(\tan(C)=\frac{AB}{BC}\).

Step2: Calculate the tangent value

Substitute \(AB = 3\) and \(BC = 6\) into the tangent formula: \(\tan(C)=\frac{3}{6}=0.5\).

Step3: Find the angle

To find the measure of \(\angle C\), we take the arctangent (inverse tangent) of \(0.5\). So, \(m\angle C=\arctan(0.5)\). Using a calculator, \(\arctan(0.5)\approx26.6^{\circ}\) (rounded to the nearest tenth).

Answer:

\(26.6\)