Question

right triangle has a side of 20 and a angle of 35
what is the value of x

Answer 1

hypotenuse

Answer 2

To solve for \( x \) in a right triangle with one side measuring 20 and an angle of 35 degrees, we need to establish which side \( x \) corresponds to. The sides of a right triangle can be categorized as:

- The side opposite the angle
- The adjacent side to the angle
- The hypotenuse

Let's analyze the possibilities:

1. **If the side of 20 is the opposite side:**
- We can use the sine function:
\[
\sin(35^\circ) = \frac{\text{opposite}}{\text{hypotenuse}} \rightarrow \sin(35^\circ) = \frac{20}{x}
\]
- Hence we can solve for \( x \):
\[
x = \frac{20}{\sin(35^\circ)}
\]

2. **If the side of 20 is the adjacent side:**
- We can use the cosine function:
\[
\cos(35^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} \rightarrow \cos(35^\circ) = \frac{20}{x}
\]
- Thus, we can solve for \( x \):
\[
x = \frac{20}{\cos(35^\circ)}
\]

3. **If the side of 20 is the hypotenuse:**
- We can use the sine and cosine functions to find the lengths of the opposite and adjacent sides:
- Opposite side:
\[
\text{opposite} = 20 \cdot \sin(35^\circ)
\]
- Adjacent side:
\[
\text{adjacent} = 20 \cdot \cos(35^\circ)
\]

Please specify which side corresponds to the 20-unit length: is it the opposite side, the adjacent side, or the hypotenuse? Once I know that, I can provide a specific calculation for \( x \).