Consider a right triangle with leg b = 7.1 and opposite angle B = 39.3. Using a calculator, determine the other angle and the remaining sides of the triangle. Express your answers using at least one decimal place.

i. a = 8.7, b = 7.1 and c = 11.2

ii. A = , B = and C =

Step-by-step explanation:

Given a right triangle with, b = 7.1 and B = .

I. Applying the trigonometric function to determine leg a, we have;

Tan θ =

Tan =

a =

  = 8.675

The length of leg a is 8.7.

ii. To determine leg c,

Sin =

              =

⇒c =

     = 11.21

The length of leg c is 11.2.

iii. Given that: B = and C =

Then,

A + B + C =  (sum of angles at a point)

A + + =

A + =

A = -

  =

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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