Question

question 2 (1 point)
for the given triangle, sin a is equal to which expression?
20 cm
15 cm
a
a) \\( \frac { 3 } { 5 } \\)
b) \\( \frac { 4 } { 3 } \\)
c) \\( \frac { 3 } { 4 } \\)
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) \(\frac{4}{5}\)