Question

find the sine of ∠b. simplify your answer and write it as a proper fraction, improper fraction, or whole number. sin(b) =

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 3\) and \(b=4\). So \(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\).

Step2: Calculate sine of angle B

The sine of an angle in a right - triangle is defined as \(\sin(B)=\frac{\text{opposite}}{\text{hypotenuse}}\). The side opposite to \(\angle B\) is \(AC = 4\) and the hypotenuse \(BC=5\). So \(\sin(B)=\frac{4}{5}\).

Answer:

\(\frac{4}{5}\)