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.
You might be interested in
Answer:
The inner function is and the outer function is
.
The derivative of the function is .
Step-by-step explanation:
A composite function can be written as , where
and
are basic functions.
For the function .
The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.
Here, we have inside parentheses. So
is the inner function and the outer function is
.
The chain rule says:
It tells us how to differentiate composite functions.
The function is the composition,
, of
outside function:
inside function:
The derivative of this is computed as
The derivative of the function is .