Question

howard is designing a chair swing ride. the swing ropes are 4 meters long, and in full swing they tilt in an angle of 23°. howard wants the chairs to be 3.5 meters above the ground in full swing. how tall should the pole of the swing ride be? round your final answer to the nearest hundredth. meters

Explanation:

Step1: Find vertical component of rope

Using cosine, vertical length \( = 4\cos(23^\circ) \). Calculate \( \cos(23^\circ) \approx 0.9205 \), so \( 4 \times 0.9205 \approx 3.682 \) m.

Step2: Add chair height to vertical rope

Pole height \( = 3.682 + 3.5 = 7.182 \), round to nearest hundredth.

Answer:

7.18