The ratio of three numbers is 4 : 3 : 1. the sum of the numbers is 64. the greatest of these three numbers is

The greatest number is 32 .

Step-by-step explanation:

As given

The ratio of three numbers is 4 : 3 : 1.

The sum of the numbers is 64.

Let us assume that the x be the scalar multiple of the numbers .

First number = 4x

Second number = 3x

Third number = x

Than the equation becomes

4x + 3x + x =  64

8x = 64

x = 8

Thus

First number = 4x

                     = 4 × 8

                     = 32

Second numbers = 3x

                             = 3 × 8

                             = 24

Third number = x

                       = 8

Therefore the greatest number is 32 .

Explanation :

It is given that,

An observer (O) spots a bird flying at a 55 degree angle from a line drawn horizontal to its nest. If the distance from the observer (O) to the bird (B) is 15,000 ft.

The attached figure shows the whole description. We need to find the distance between bird and the nest. Let it is equal to x.

Using trigonometric identities as :

x = 8603.64 feet

or

x = 8604 feet

So, the bird is 8604 feet far from its nest. Hence, this is the required solution.