Question

Use ABC, in which AB = 48, AC = 64, and BC = 80, to answer the question.

B
80
48.
A
64
С
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What is the ratio for cos B?

Answer 1

`CosB = (48)/(80)`

Explanation:

Given

AB = 48, AC = 64, and BC = 80

Required

Determine the ratio of cosB

The first step is to determine, which type of triangle it is.

Checking for Right Angled Triangle

For a triangle to be a right angled triangle, the square of the largest side must be equal to the sum of squares of other sides

This implies that:

`80^2 = 48^2 + 64^2`

`6400 = 2304 + 4096`

`6400 = 6400`

Hence, the triangle is a right angled triangle [See attachment]

From trigonometry;

`CosB = (Adjacent)/(Hypotenuse)`

The adjacent of B = 48 while the hypotenuse is 80;

Hence;

`CosB = (48)/(80)`

Hence, the ratio of cos B is
`CosB = (48)/(80)`