If the polygon Z has the area of 9. The scale factor between Z and Z is 2. What is the area of Z?

zhenek [66]

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the ∠BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠CAB is AC

∵ The opposite side to ∠CAB is BC

∵ AB = 13 units ⇒ hypotenuse

∵ CB = 12 units ⇒ opposite

∵ AC = 5 units ⇒ adjacent

- Let us find the trigonometry ratios of angle BAC

∵ m∠CAB is x

∵ $sin(x)=\frac{BC}{AB}$

∴ $sin(x)=\frac{12}{13}$

∴ $x=sin^{-1}(\frac{12}{13})$

∵ $cos(x)=\frac{AC}{AB}$

∴ $cos(x)=\frac{5}{13}$

∴ $x=cos^{-1}(\frac{5}{13})$

∵ $tan(x)=\frac{BC}{AC}$

∴ $tan(x)=\frac{12}{5}$

∴ $x=tan^{-1}(\frac{12}{5})$

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

4 0

3 years ago

Read 2 more answers

Item 7

topjm [15]

Answer:8,5 recirpoal is 5,8

Step-by-step explanation:

8 0

3 years ago

What is the measure of ZBAQ 1 B 84 0 x 140

Dahasolnce [82]

Answer:

117.600

Step-by-step explanation:

7 0

3 years ago

On a coordinate plane, 2 polygons are shown. Polygon A B C D has points (negative 3, 3), (5, 3), (5, negative 1), and (1, negati

ad-work [718]

Answer:

A dilation with a scale factor of One-fourth and then a translation

Step-by-step explanation:

Plot points A, B, C, D, A', B, C' and D' on the coordinate plane and draw quadrilaterals ABCD and A'B'C'D'.

These quadrilaterals are similar and quadrilateral a'B'C'D' has sides 4 times smaller than quadrilateral ABCD.

This means that the dilation with a scale factor of one-fourth was performed.

The figures were not rotated (they have the same positions), so the second transformation was translation.

Hence, correct option is B: a dilation with a scale factor of One-fourth and then a translation

5 0

3 years ago

Read 2 more answers

A park has a large circle painted in the middle of the playground area.thecircle is divided into 4 equal sections And each secti

lilavasa [31]

Answer:

The area of each section of the circle is $25\pi\ m^{2}$

Step-by-step explanation:

we know that

The area of a circle is equal to

$A=\pi r^{2}$

we have

$r=10\ m$

substitute

$A=\pi (10^{2})=100\pi\ m^{2}$

To find the area of each section divide the complete area of the circle by $4$

so

$100\pi\ m^{2}/4=25\pi\ m^{2}$

8 0

4 years ago