1. **State the problem:** We have a right triangle JIH with a right angle at vertex I. Given: - Segment IH = 20 - Angle at H = 49° - Segment JH = x (unknown) We need to find the length of segment JH (x). 2. **Identify the sides relative to angle H:** - IH is adjacent to angle H - JH is the hypotenuse 3. **Use the cosine function:** The cosine of an angle in a right triangle is the ratio of the adjacent side over the hypotenuse: $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$ Here, $$\theta = 49^\circ$$, adjacent = IH = 20, hypotenuse = x. So, $$\cos(49^\circ) = \frac{20}{x}$$ 4. **Solve for x:** Multiply both sides by x: $$x \cos(49^\circ) = 20$$ Divide both sides by $$\cos(49^\circ)$$: $$x = \frac{20}{\cos(49^\circ)}$$ Intermediate step showing cancellation: $$x = \frac{20}{\cancel{\cos(49^\circ)}} \times \frac{1}{\cancel{\cos(49^\circ)}}$$ 5. **Calculate the value:** $$\cos(49^\circ) \approx 0.6561$$ So, $$x = \frac{20}{0.6561} \approx 30.5$$ 6. **Final answer:** The length of segment JH is approximately **30.5** units.