Dr. Johnny Smith is looking up from camp at an angle of elevation of 27 degrees to the top of a Red Wood Tree. The tree is 85 feet tall. What is
the distance from the bottom of the tree to the camp?

166.8 feet

Step-by-step explanation:

tan = opp/adj

opp = height of tree

adj = distance

tan27 = 85/distance

distance = 85/tan27

use calculator

distance = 166.821892967937799

166.8 feet

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.