The base of a 35 foot ladder is 15 feet from a tree. If the ladder leans against the tree , what is the angle of elevation ?

About 31.62 feet is the elevation

Step-by-step explanation:

Use pythagoream theorem

So we know 35 is the hypotnuse because if it leans against the tree and it’s 35 feet, its the slant of the triangle which is the hypotnuse

15 is one side

So just fill it in

15^2+b^2=35^2

Now

225+b^2=1225

Now subtract 225 on both sides

b^2=1000

Now find the square root

31.62

Final answer about 31.62

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.