Answer:
x is approximately 226.3 feet
y is approximately 308.6 feet
z is approximately 226.3 feet
Step-by-step explanation:
The given parameters of the walls are;
The angle of elevation from the top of the shorter wall to the top of the opposing wall, θ₁ = 20°
From the diagram, the angle of depression from the top of the shorter wall to the bottom of the opposing wall, θ₂ = 45°
The distance from the bottom of the shorter wall to the base of the opposing wall, l = 320 feet
x = The height of the shorter wall = l × sin(θ₂)
∴ x = 320 feet × sin(45°) = 320 feet × (√2)/2 = 160·√2 feet ≈ 226.3 feet
∴ x ≈ 226.3 feet
By observation, we have;
y = x + z × tan(θ₁)
Where;
z = l × cos(θ₂)
∴ y = 160·√2 + 320 × cos(45°) × tan(20°) ≈ 308.6
y ≈ 308.6 feet
z = l × cos(θ₂)
∴ z = 320 × cos(45°) = 160·√2 ≈ 226.3
z ≈ 226.3 feet.
y = 80x - 60
Answer is B. y = 80x - 60
Double check:
When x = 1, y = 80(1) - 20 = 80 -60 = 20
When x = 2, y = 80(2) - 20 = 160 -60 = 100
When x = 3, y = 80(3) - 20 = 240 -60 = 180
When x = 4, y = 80(4) - 20 = 320 -60 = 260
When x = 5, y = 80(5) - 20 = 400 -60 = 340
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