Question

question 31 (1 point)
for the given triangle, sin a is equal to which expression?
20 cm
15 cm
a) 3/4
b) 4/3
c) 3/5
d) 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) \(\frac{4}{5}\)