Question

solve for x. Round to the nearest tenth, if necessary. the hypotenuse is 5 and the angle is 35 the opposite is x

Answer 1

To solve for \( x \), the length of the opposite side in a right triangle where the hypotenuse is 5 and the angle is 35 degrees, we can use the sine function. The sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse.

The formula is given by:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this case, we will rearrange the formula to solve for \( x \):

\[
x = \text{hypotenuse} \times \sin(\theta)
\]

Substituting the given values:

\[
x = 5 \times \sin(35^\circ)
\]

Now, let's calculate \( \sin(35^\circ) \):

Using a calculator, we find that:

\[
\sin(35^\circ) \approx 0.5736
\]

Now substitute this value back into the equation for \( x \):

\[
x = 5 \times 0.5736 \approx 2.868
\]

Rounding to the nearest tenth, we have:

\[
x \approx 2.9
\]

Thus, the length of the opposite side \( x \) is approximately **2.9**.