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1 year ago

32. Find the ratio of the side lengths of the small triangle to the large

Mathematics

1 answer:

kupik [55]1 year ago

8 0

Answer:

2/3

Step-by-step explanation:

that the ratio of that number

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Use the given information to find the exact value of the trigonometric function

eimsori [14]

$\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}$

Half Angle Formula

$\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}$ $\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}$ $\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}$ $\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\ \\ \end{gathered}$

Answer:

$\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}$

Checking:

$\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{ (3rd quadrant)} \end{gathered}$

Also,

$\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}$

The answer is none of the choices

7 0

10 months ago

PLEASE CAN SOMEONE HELP IM SO DESPERATE IVE BEEN STUCK ON THIS FOREVER

Maru [420]

Answer:

0.34

Step-by-step explanation:

The total probability is equal to one.

P (Dr. Green) = 1 - (0.25 + 0.17 + 0.21 + 0.03)

= 1 - 0.66

= 0.34

3 0

2 years ago

Read 2 more answers

10) Solve the equation for the variable "a":<br> 2(x + a) = 4b

masya89 [10]

Answer:

a= 2b-x

Step-by-step explanation:

You have to isolate the variable by dividing each side of the factors that does not contain the variable "a".

3 0

3 years ago

after the interview ,Ellen decided to hire two of the applicants and reject the others .Ellen's assistant called back the applic

Elden [556K]

Answer:

40 + 2r

Step-by-step explanation:

Well an hour has 60 minutes.

So 60 x 1/30 = 60/30 = 2 minutes for each person that didn't get into the job

60 x 1/3 = 60/3 = 20 minutes for the people that made it into the job.

20 x 2 = 40 minutes in total for the people that made it into the job.

We don't know how much people got rejected so:

The answer is

40 + 2r

7 0

2 years ago

PLZZZZ HELPP WILL GIVE BRAINLIEST

liberstina [14]

Answer:

Step-by-step explanation:

Since both triangles are right angle triangles that means one angle is 90°. other two sides are given congruent .

that means lengths of hypotenuse and the leg of the one right angle triangle is equal to the corresponding other hypotenuse and leg of other triangle.

This fulfills the condition of HL congruency.

7 0

2 years ago