find sinθ, where θ is the angle shown. give an exact value, not a decimal approximation.
find sinθ, where θ is the angle shown. give an exact value, not a decimal approximation.
Answer
Explanation:
Step1: Recall sine - definition
In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
Step2: Identify opposite and hypotenuse
The side opposite to angle $\theta$ has length $ \sqrt{8^{2}-3^{2}}=\sqrt{64 - 9}=\sqrt{55}$ (by the Pythagorean theorem $a=\sqrt{c^{2}-b^{2}}$, where $c = 8$ is the hypotenuse and $b = 3$ is the given side), and the hypotenuse $c = 8$.
Step3: Calculate $\sin\theta$
$\sin\theta=\frac{\sqrt{55}}{8}$
Answer:
$\frac{\sqrt{55}}{8}$