Question

Find θ in the given right angle where opposite side is 6 and hypotenuse is 10
round your answer to 2 decimal places
θ = _____ degrees

Answer 1

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:

\[
\theta = 36.87 \text{ degrees}
\]