Question

What is this sign of 30ﾟ angle and the sign of the 60ﾟ angle

Answer 1

We are asked to find out the values of sine 60° and sine 30°

Recall from the trigonometric ratios,

`\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}`

From the given triangle,

With respect to angle 60°, the opposite side is 25√3 ft and the hypotenuse is 50 ft.

Let us substitute these values into the above sine ratio

`\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 60\degree=\frac{25\sqrt[]{3}}{50} \\ \sin 60\degree=\frac{\sqrt[]{3}}{2} \end{gathered}`

So, the value of sine 60° is √3/2

From the given triangle,

With respect to angle 30°, the opposite side is 25 ft and the hypotenuse is 50 ft.

Let us substitute these values into the above sine ratio

`\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin 30\degree=(25)/(50) \\ \sin 30\degree=(1)/(2) \end{gathered}`

So, the value of sine 30° is 1/2

Therefore, the sine of 60ﾟ angle is √3/2 and the sine of 30ﾟ angle is 1/2