Question

Solve for the missing side. Round to the nearest tenth. (1 point) Responses 3.9 3.9 5.7 5.7 4.5 4.5 27.0. X length, 24 degrees width, 11 angle. just do the equation 2 answers

Answer 1

10 is not a option

Answer 2

To solve for the missing side (X) in a right triangle, we can use the given angle (24 degrees) and the length of the side opposite to that angle (11 units). Given that this is a right triangle, we can apply the sine function for opposite side (X) and hypotenuse (11).

The sine function is defined as follows:

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

Thus, for our triangle, we can rearrange the equation to solve for the opposite side (X):

\[
X = \text{hypotenuse} \cdot \sin(\theta)
\]

Substituting the values we have:

\[
X = 11 \cdot \sin(24^\circ)
\]

Calculating \( \sin(24^\circ) \) (using a calculator):

\[
\sin(24^\circ) \approx 0.4067
\]

Now plug that back into the equation for X:

\[
X \approx 11 \cdot 0.4067 \approx 4.4737
\]

Rounding to the nearest tenth, we get:

\[
X \approx 4.5
\]

Now, if you need another angle (for example, the adjacent side using cosine), we can calculate it as well:

Using the cosine function for adjacent side (A):

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]
\[
A = \text{hypotenuse} \cdot \cos(\theta)
\]

Substituting values:

\[
A = 11 \cdot \cos(24^\circ)
\]

Calculating \( \cos(24^\circ) \):

\[
\cos(24^\circ) \approx 0.9063
\]

Now plug that back into the equation for A:

\[
A \approx 11 \cdot 0.9063 \approx 9.9693
\]

Rounding to the nearest tenth, we get:

\[
A \approx 10
\]

So the two answers for the missing side (considering the opposite side and adjacent) are:

1. \( X \approx 4.5 \)
2. \( A \approx 10 \)