What is the approximate length?

Mathematics

1 answer:

Usimov [2.4K]2 years ago

4 0

9514 1404 393

Answer:

(a) 75.5

Step-by-step explanation:

There are two ways you can work this.

Pythagorean theorem

Triangle CMP is a right triangle. CM = AC = 55. CP = CB -PB = 55 -15 = 40. Then length PM can be found from ...

PM² +CP² = CM²

PM = √(CM² -CP²) = √(55² -40²) = √1425 ≈ 37.749

The length MN is twice the length of PM, so is ...

MN = 2×PM = 2×37.349 = 75.498

The length of MN is about 75.5.

Using chord relationships

The products of the different lengths for the same chord are the same for the crossed chords.

AP×PB = MP×PN

We know MP = PN, so ...

MP = √(AP×PB) = √((55+40)(15)) = √1425

As before, MN = 2×MP = 2√1425

MN ≈ 75.5

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Pythagorean Theorem
$a^{2}$ + $b^{2}$ = $c^{2}$
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