To find the angle θ in a right triangle where the opposite side is 6 and the hypotenuse is 10, you can use the sine function, which is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Plugging in the values:
\[ \sin(\theta) = \frac{6}{10} = 0.6 \]
Next, we need to find θ by taking the inverse sine (arcsin) of 0.6:
\[ \theta = \arcsin(0.6) \]
Using a calculator, we find:
\[ \theta \approx 36.87 \text{ degrees} \]
Rounding to two decimal places, we have:
\[ \theta \approx 36.87 \text{ degrees} \]
So, the answer is:
\[ \theta = 36.87 \text{ degrees} \]