Atower casts a shadow that is 60 feet long when the angle of elevation of the sun is 65˚. how tall is the tower?

128.67 ft

Step-by-step explanation:

Topic: Trigonometric Functions

You should be familiar with the concept of trigonometric functions because this topic involves degrees of traingles with the lenght of their sides, as you can see in the image, you need to remember which trigonometric function involves both sides (not hypotenuse) of a triangle, let's review

O= opposite, A = adjacent, H = Hypotenuse, α = 65°

sen (α) =

cos(α) =

tan(α) =

guess which of them works? yeah its tan(α), so we have that

tan(65°) =

findig h in the previous equation we have that

60 ft * tan(65°) = h

computing in a calculator it means that the height (h) of the tower is

h = 128. 67 ft

2 x t divided by n

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt