Answer:
The north - south distance across swan lake is 8 km
Step-by-step explanation:
Look to the attached figure
Kendra's house and the distances between it and the North tip, southern tip of swan lake formed a right Δ
∵ Kendra lives 10 Km from the northern tip of swan lake
- That means the length of the hypotenuse of the right Δ is 10
∴ The hypotenuse of the right Δ = 10
∵ Kendra lives 6 Km from the southern tip of swan lake
- That means the length of the horizontal leg of the right Δ is 6
∴ The horizontal leg = 6
- By using Pythagoras Theorem
∵ (hypotenuse)² = (H.leg)² + (V.leg)²
∴ (10)² = (6)² + (x)²
∴ 100 = 36 + x²
- Subtract 36 from both sides
∴ 64 = x²
- Take √ for both sides
∴ 8 = x
∴ The vertical leg of the right triangle = 8
∵ x represents the north-south distance across swan lake
∴ The north - south distance across swan lake is 8 km
