Kayson is looking at two buildings, building A and building B, at an angle of elevation of 59°. Building A is 40 feet away, and building B is 60 feet away. Which building is taller and by approximately how many feet? Building A; it is around 66.57 feet taller than building B
Building A; it is around 33.29 feet taller than building B
Building B; it is around 66.57 feet taller than building A
Building B; it is around 33.29 feet taller than building A

D. Building B is taller by 33.29 feet aller than building A

Step-by-step explanation:

B is taller and further away. Draw this to see. Closer things look bigger, so if the buildings have the same angular elevation from one spot, the taller building is further away. The hypotenuse touches the top of building A and keeps on going at the same angle to building B, further away.

tan B=ht/60

ht B=60 tan 59=99.86 ft.

The last choice, Building B is taller by 33.29 ft

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.