Question

Find sine, where is the angle shown. Give an exact value, not a decimal approximation. sine = 1 7

Answer 1

We are asked to find the value of sinθ

Recall from the trigonometric ratios,

`\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}`

Since it is a right-angled triangle, we can find the length of the third side by using the Pythagorean theorem.

`\begin{gathered} a^2+b^2=c^2 \\ a^2=c^2-b^2 \\ a^2=25^2-7^2 \\ a^2=625-49 \\ a^2=576 \\ a=\sqrt[]{576} \\ a=24 \end{gathered}`

Now we can find the value of sinθ

`\sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}}=(24)/(25)=0.96`

Therefore, the value of sinθ is

`\sin \theta=(24)/(25)`