A student visiting the Sears Tower Skydeck is 1353 feet above the ground. Find the distance the student can see to the horizon.
Use the formula to approximate the distance d in miles to the horizon when h is the height of the viewer’s eyes above the ground in feet. Round to the nearest mile. A. 45 miles B. 601 miles C. 36 miles D. 1010 Miles
2 answers:
Answer:
Option A. 45 miles
Step-by-step explanation:
A student visiting the Sears Tower Skydeck is 1353 feet or 0.25625 miles above the ground.
We have to find the distance the student can see to the horizon.
We can see in the figure attached r is the radius of the earth.
h is the height of the tower and x is the distance to the horizon.
Now we can calculate the distance x by applying Pythagoras theorem in right angle ΔTOH. (Radius of the earth OH ⊥ tangent distance to the horizon TH)
(h + r)² = r² + x²
By putting the values in the formula
h = height of the tower = 0.25625 miles
r = radius of the earth = 3958.8 miles
(3958.8 + 0.25625)²= x² + (3958.8)²
x² = (3959.05)² - (3958.80)²
x² = 15674126.40 - 15672097.40
x² = 2029
x = √2029
x = 45.04 ≈ miles.
Therefore Option A. 45 miles is the answer.
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