The following table represents the altitude of a hiker climbing in Mountain over a 60 minute hike. Calculate the average rate of
change over the interval from 0 to 30 minutes.
A: The rate of change is about 90 feet per minute.
B: The rate of change is about 3 feet per minute.
C: The rate of change is about 2 feet per minute.
D: The rate of change is about 30 feet per minute.
A: The rate of change is about 90 feet per minute.
B: The rate of change is about 3 feet per minute.
C: The rate of change is about 2 feet per minute.
D: The rate of change is about 30 feet per minute.
1 answer:
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Answer:
174.6 ft
Step-by-step explanation:
It can be helpful to draw a diagram of the triangle we're concerned with. (See attached.)
We know the angle at the end of the shadow inside the triangle is 52°-22° = 30°. We assume the tree is growing straight up out of the hillside, so its angle with the hill inside the triangle is 90°+22° = 112°. Then the remaining angle between the shadow and the tree at the top of the tree is ...
180° -30° -112° = 38°
Now, we have the angle opposite the tree, and the angle opposite the known side length of the triangle (215 feet along the hill, AC in the diagram). This is enough information to usefully use the Law of Sines.
c/sin(C) = a/sin(A)
c = a(sin(C)/sin(A)) = (215 ft)(sin(30°)/sin(38°)) ≈ 174.6 ft
The height of the tree is about 174.6 feet.
