To the nearest degree, find an approximate measure of the angle of elevation to the sun when a tree whose height is 32 meters casts a shadow 35 meters long. Enter a number answer only.

Step-by-step explanation:

the angle of elevation is the angle on the ground at the end of the shadow abs aiming towards the sun.

we know one angle : the 90° between the tree and its shadow (on the ground).

so, we can calculate with Pythagoras the length of the line of sight bergen the end of the shadow and the top of the tree, which is the Hypotenuse of this right-angled triangle.

Hypotenuse² = 32² + 35² = 1024 + 1225 = 2249

Hypotenuse = sqrt(2249) = 47.42362281... m

the height of the tree is the sine of the angle of elevation multiplied by the length of the Hypotenuse (as the radius of the virtual circle).

32 = sin(angle) × sqrt(2249)

sin(angle) = 32/sqrt(2249) = 0.6747692...

angle of elevation = 42.43622979...° ≈ 42°

step-by-step explanation:

f

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.