In a right triangle, if sin θ = 3/5, what is θ approximately?

In a right triangle, if sin θ = 3/5, what is θ approximately?

• A. 36.87 degrees
• B. 53.13 degrees
• C. 30 degrees
• D. 45 degrees

Answer: (A)

Think in terms of what sine means in a right triangle: sine is opposite over hypotenuse. If sin θ = 3/5, you can picture a triangle where the side opposite θ is 3 and the hypotenuse is 5. The remaining leg then is sqrt(5^2 − 3^2) = sqrt(16) = 4. With opposite 3 and hypotenuse 5, the angle θ has a value whose sine is 3/5, which is arcsin(0.6). That comes out to about 36.87 degrees. The other acute angle in the triangle would be 90 − 36.87 ≈ 53.13 degrees, but its sine is 4/5, not 3/5, so it doesn’t fit the given condition. Therefore the angle is approximately 36.87 degrees.

Think in terms of what sine means in a right triangle: sine is opposite over hypotenuse. If sin θ = 3/5, you can picture a triangle where the side opposite θ is 3 and the hypotenuse is 5. The remaining leg then is sqrt(5^2 − 3^2) = sqrt(16) = 4. With opposite 3 and hypotenuse 5, the angle θ has a value whose sine is 3/5, which is arcsin(0.6). That comes out to about 36.87 degrees. The other acute angle in the triangle would be 90 − 36.87 ≈ 53.13 degrees, but its sine is 4/5, not 3/5, so it doesn’t fit the given condition. Therefore the angle is approximately 36.87 degrees.