Aright triangle abc is shown. using any trigonometric ratio, find the measure of angle c to the nearest degree.

Angle C = 28°

Solution:

SinQ = Opp/hyp

SinQ = 8/17

Q = Sin-¹(8/17)

Q = 28.07248694

Q = 28(nearest degree)

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.