According to this diagram, what is sin 28 degrees?

Check the final answer first, then review the worked steps.

Problem

According to this diagram, what is sin 28 degrees?

Answer

\(8/17\)

Step-by-step solution

  1. Identify the trigonometric ratio: The problem asks for the sine of an angle. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
  1. Identify the angle: The angle in question is $28^\circ$.
  1. Identify the side opposite the angle: In the given diagram, the side opposite the $28^\circ$ angle has a length of 8.
  1. Identify the hypotenuse: The hypotenuse is the longest side of the right-angled triangle, which is opposite the right angle ($90^\circ$). In this diagram, the hypotenuse has a length of 17.

5. Calculate the sine: Using the definition of sine, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$:
$$\sin(28^\circ) = \frac{8}{17}$$