Two of the angles in a triangle measure 52 and 22 what must be the measure of the third angle

help The screen in a theatre is 22 ft high and is positioned 10 ft above the floor, which is flat. The first row of seats is 7 f

Stella [2.4K]

<span>(a.)
Let's say α is the angle that subtends from the top of the screen to horizontal eye-level.
Let β be the angle that subtends from the bottom of the screen to horizontal eye-level.

tanα = (22 + 10 - 4) / x = 28/x
α = arctan(28/x)

tanβ = (10 - 4) / x = 6/x
β = arctan(6/x)

Ɵ = α - β
Ɵ = arctan(28/x) - arctan(6/x)

(b.)
tanƟ = tan(α - β) = (tanα - tanβ) / (1 + tanα tanβ)
tanƟ = (28/x - 6/x) / [1 + (28/x)(6/x)]
tanƟ = (22/x) / [1 + (168/x²)]
tanƟ = 22x / (x² + 168)
Ɵ = arctan[22x / (x² + 168)]</span>

4 0

3 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

What’s the volume and surface area

KiRa [710]

Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

6 0

3 years ago

The ratio of the number of left handers to the number of right handers in a middle school is 6:15. If there are 120 left handers

omeli [17]

Answer:

300 right handers

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

1) make c the subject of of the formula v=c/4-5

alisha [4.7K]

Answer:

1)c = -v 2)(q-5)/4

Step-by-step explanation:

v = c/4-5

v = c/-1

c = -v

q-p=3p+5

q = 4p+5

q-5 = 4p

p = (q-5)/4

8 0

2 years ago