Question

find sinθ, where θ is the angle shown. give an exact value, not a decimal approximation.

Explanation:

Step1: Find hypotenuse length

By 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: Use sine - definition

The definition of $\sin\theta$ in a right - triangle is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the opposite side to $\theta$ is 4 and the hypotenuse is 5. So $\sin\theta=\frac{4}{5}$.

Answer:

$\frac{4}{5}$