Mathematics: What is the area of the sector ?

What is the area of the sector ? - id5762222, Cheyanne5627

fatherbamboo

22.01.2022

They forget to say "not to scale". I'm guessing this is trig because I don't see another way to do it.

Let's consider x=chord PQ first. By the Law of Cosines

$x^2 = 3^2 + 5^2 - 2(3)(5) \cos 81^\circ = 34 - 30\cos 81^\circ$

We have an isosceles triangle formed by two radii of 9 cm and x=PQ. By the Law of Cosines again,

$x^2 = 9^2 + 9^2 - 2(9)(9) \cos B$

$x^2 = 162 - 162 \cos B$

$\cos B = \dfrac{162 - x^2}{162} = 1 - \dfrac{x^2}{162}$

$\cos B = 1 - \dfrac{34 - 30\cos 81^\circ}{162}$

$B = \arccos \left(1 - \dfrac{34 - 30\cos 81^\circ }{162} \right)$

The area of the circle is the fraction given by the angle,

$A = \dfrac{B}{360^\circ} \pi r ^2$

$A \approx \dfrac{ \arccos \left(1 - \dfrac{34 - 30\cos 81^\circ}{162} \right) }{360} (3.142)9^2$

$A\approx 24.7474332960707$

24.7 sq cm

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miathegeek97

29.06.2020

Answer

B) associative property of addition

Explanation

The associative property states that you can add or multiply regardless of how the numbers are grouped.

For example:

3 + 5 = 8

5 + 3 = 8

Both equations are giving you 8 as the answer. This is called associative property of addition.

∴ 5 + 3w + 2 = 5 + 2 + 3w ⇒ represent the associative property of addition.

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