Find the Exact Value sin(53 degrees )

Problem

sin(53)

Solution

1. Identify the angle 53 as a common approximation used in physics and geometry for a right triangle with side lengths in the ratio 3:4:5

2. Recall that in a 3−4−5 right triangle, the interior angles are approximately 36.87 and 53.13

3. Relate the sine function to the ratio of the side opposite the angle to the hypotenuse.

4. Determine that for the angle 53.13 (often rounded to 53 in textbook problems), the opposite side is 4 and the hypotenuse is 5

5. Calculate the ratio.

sin(53)≈4/5

Final Answer

sin(53)=4/5

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