Please help me with this system of equations problem
1 answer:
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Answer:
148ft
Step-by-step explanation:
To solve this question, you'll have to imagine the statue makes a right angle triangle with the base since it has an angle of elevation from the base to the top of the torch.
Assuming the height from the pedestal to the top of the torch is y
The height of the statue is x
But we know the height of the pedestal = 150ft
The distance from the observer to the base of the pedestal = 250ft
And the angle of elevation = 50°
See attached document for better illustration.
Tanθ = opposite / adjacent
θ = 50°
Adjacent = 250
Opposite = y
Tan50 = t / 250
y = 50 × tan50
y = 50 × tan50
y = 50 × 1.1917
y = 297.925ft
The height of the statue from the base of the pedestal to the top of the torch is 297.925ft
The height of the statue = x
x = (height of the statue + height of the pedestal) - height of the pedestal
x = y - 150
x = 297.925 - 150
x = 147.925ft
Approximately 148ft
The height of the statue is 148ft
