Question

what is m∠a? you may round your answer to one decimal place.
enter deg after any value that is in degrees.

Explanation:

Step1: Identify trigonometric ratio

In right triangle \(ABC\) (right-angled at \(C\)), to find \(m\angle A\), we can use the sine, cosine, or tangent ratio. Let's use sine: \(\sin(A)=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite \(\angle A\) is \(BC = 4\), and the hypotenuse \(AB = 10\). So \(\sin(A)=\frac{4}{10}=0.4\).

Step2: Calculate angle \(A\)

To find \(A\), we take the inverse sine (arcsin) of \(0.4\). Using a calculator, \(A=\arcsin(0.4)\). Calculating this, we get \(A\approx23.6^\circ\) (rounded to one decimal place).

Answer:

\(23.6\) deg