In the given right triangle, one leg is 20 and one acute angle is 70 degrees. Find the length of the hypotenuse, x.

We have a right-angled triangle.

• The angle given is $70^\circ$.
• The side opposite to the $70^\circ$ angle is 20.
• The hypotenuse (the side opposite the right angle) is labeled 'x'.

Since we know the side opposite the given angle and we want to find the hypotenuse, we use the sine function:

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

Multiply both sides by x:

$$x \cdot \sin(70^\circ) = 20$$

Divide both sides by $\sin(70^\circ)$:

$$x = \frac{20}{\sin(70^\circ)}$$

Using a calculator, $\sin(70^\circ) \approx 0.9397$.

$$x \approx \frac{20}{0.9397}$$ $$x \approx 21.283$$

The value of x is 21.28.