Question

Is it true or false that for any right triangle with a \(30^{\circ}\) angle, \(\sin 30^{\circ}=0.5 ?\) Explain.

Short answer

True, \(\sin 30^{\circ}\) is indeed 0.5.

Step-by-step solution

Concept of Trigonometric Ratios

Recall that in a right triangle, the sine of an angle is defined as the ratio of the side opposite the angle to the hypotenuse.

Value of Sin(30)

Consider a right triangle with one angle of 30 degrees. The side opposite to the 30 degrees angle is half of the hypotenuse. Therefore, the sine of 30 degrees, which is the ratio of the opposite side over the hypotenuse, will be 0.5.

Conclusion

So, it is true that for any right triangle with a 30 degrees angle, the sine of 30 degrees is 0.5.