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Irina-Kira [14]
2 years ago
8

PLEASE HELP ITS DUE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
BaLLatris [955]2 years ago
5 0

Hello!

1. To figure out the angle measurement when given two other angles from the triangle, it's important to realize that any given triangle's angles will add up to 180.

Since 25 and 52 is given to us, let's subtract 180-25-52 to get 103; this is the angle measurement of 3.

2. Assuming ray LAP is a straight line, we can conclude that 3 and 4 are supplementary angles in which they add up to 180 degrees (line).

Since we know the value for 3, we just need to subtract that from 180, the angle measurement of the line.

180-103=77; angle 4 is measured at 77 degrees

3. The angle's relationship for angles 1, 2, and 3 are correlated. Since they are a triangle, they will always add up to 180 degrees exactly; angles 2 and 3 also equal angle 4. Angle 3 and 4 are supplementary angles, which means they are two angles intersected by a ray.

4. Angles 2 and 3 from the triangle equal angle 4. This works out because those two angles add up to the angle for 4.

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Step-by-step explanation:

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The drama club was selecting which carnival booths to sponsor at the fall carnival from a list of nine. How many different ways
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8 0
2 years ago
9. A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?
SSSSS [86.1K]

Answer:

Part 4) r=84\ units

Part 9) sin(\theta)=-\frac{\sqrt{5}}{3}

Part 10) sin(\theta)=-\frac{9\sqrt{202}}{202}

Step-by-step explanation:

Part 4) A circle has an arc of length 56pi that is intercepted by a central angle of 120 degrees. What is the radius of the circle?

we know that

The circumference of a circle subtends a central angle of 360 degrees

The circumference is equal to

C=2\pi r

using proportion

\frac{2\pi r}{360^o}=\frac{56\pi}{120^o}

simplify

\frac{r}{180^o}=\frac{56}{120^o}

solve for r

r=\frac{56}{120^o}(180^o)

r=84\ units

Part 9) Given cos(∅)=-2/3 and ∅ lies in Quadrant III. Find the exact value of sin(∅) in simplified form

Remember the trigonometric identity

cos^2(\theta)+sin^2(\theta)=1

we have

cos(\theta)=-\frac{2}{3}

substitute the given value

(-\frac{2}{3})^2+sin^2(\theta)=1

\frac{4}{9}+sin^2(\theta)=1

sin^2(\theta)=1-\frac{4}{9}

sin^2(\theta)=\frac{5}{9}

square root both sides

sin(\theta)=\pm\frac{\sqrt{5}}{3}

we know that

If ∅ lies in Quadrant III

then

The value of sin(∅) is negative

sin(\theta)=-\frac{\sqrt{5}}{3}

Part 10) The terminal side of ∅ passes through the point (11,-9). What is the exact value of sin(∅) in simplified form?    

see the attached figure to better understand the problem

In the right triangle ABC of the figure

sin(\theta)=\frac{BC}{AC}

Find the length side AC applying the Pythagorean Theorem

AC^2=AB^2+BC^2

substitute the given values

AC^2=11^2+9^2

AC^2=202

AC=\sqrt{202}\ units

so

sin(\theta)=\frac{9}{\sqrt{202}}

simplify

sin(\theta)=\frac{9\sqrt{202}}{202}

Remember that      

The point (11,-9) lies in Quadrant IV

then      

The value of sin(∅) is negative

therefore

sin(\theta)=-\frac{9\sqrt{202}}{202}

5 0
3 years ago
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