Question

question 23 (1 point)
for the given triangle, \\( \sin a \\) is equal to which expression?
\\( \bigcirc \\) a) \\( \frac{4}{3} \\)
\\( \bigcirc \\) b) \\( \frac{3}{5} \\)
\\( \bigcirc \\) c) \\( \frac{3}{4} \\)
\\( \bigcirc \\) d) \\( \frac{4}{5} \\)

Explanation:

Step1: Find the hypotenuse

Using the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 15\) and \(b=20\).
\(c=\sqrt{15^{2}+20^{2}}=\sqrt{225 + 400}=\sqrt{625}=25\)

Step2: Use the sine formula

The formula for sine in a right - triangle is \(\sin A=\frac{\text{opposite}}{\text{hypotenuse}}\).
The side opposite to angle \(A\) is \(20\) and the hypotenuse is \(25\). So \(\sin A=\frac{20}{25}=\frac{4}{5}\)

Answer:

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