Question

See attachment.

Answer 1

what's the question though?

Answer 2

Find the value of the variable using the chart on the bottom.

Answer 3

a=42.666

Answer 4

Explain?

Answer 5

b=40

Answer 6

the triangles are all similar, and they're right triangles :)

Answer 7

Use the similarity ratio and pythagorean theorem to solve :)

Answer 8

oh okay :)

Answer 9

C=53.333

Answer 10

The square of the hypotenuse of a right triangle is equal to the sum of the squares of the two adjacent sides.

b^2 = 32^2 + 24^2
b = 40

The Pythagorean Triple (24, 32, 40) is an eight-multiple of (3,4,5) so you can get b's value that way, too.
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a is to 32 as 32 is to 24.

Because:

If the altitude is drawn to the hypotenuse of a right triangle, the length of the altitude is the geometric mean between the lengths of the segments of the hypotenuse.

a/32 = 32/24

24 a = (32)^2

a = 128/3

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If the altitude is drawn to the hypotenuse of a right triangle, the length of either leg is the geometric mean between the hypotenuse and the segment of the hypotenuse adjacent to the leg.

Because of that,

(128/3) / c = c / ( (128/3) + 24)

c = 160/3