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

Want more problems? Check here!