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Slav-nsk [51]
2 years ago
6

if a right triangle has lengths 99 inches, 101 inches and 20 inches, what is the length of the hypotenuse

Mathematics
1 answer:
Anna35 [415]2 years ago
5 0

Answer:

The hypotenuse is 10201

Step-by-step explanation:

20^2+99^2=101^2

400+9801=10201

10201=10201

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Find the six trig function values of the angle 240*Show all work, do not use calculator
-BARSIC- [3]

Solution:

Given:

240^0

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

sin240^0=sin(180+60)

Using the trigonometric identity;

sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny

Hence,

\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

cos240^0=cos(180+60)

Using the trigonometric identity;

cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny

Hence,

\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\  \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

tan240^0=tan(180+60)

Using the trigonometric identity;

tan(180+x)=tan\text{ }x

Hence,

\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\  \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}

To get cosec 240 degrees:

\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}

To get sec 240 degrees:

\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\  \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\  \\ Thus, \\ sec240^0=-2 \end{gathered}

To get cot 240 degrees:

\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\  \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}

5 0
1 year ago
Solve for A ? <br><br> Anyone willing to help me :)
GrogVix [38]

Answer:

<h2>2.2</h2>

Step-by-step explanation:

Use the cosine law:

BC^2=AB^2+AC^2-2(AB)(AC)\cos(\angle A)

We have:

BC=a\\\\AB=4\\\\AC=3\\\\m\angle A=32^o\to\cos32^o\approx0.848

Substitute:

a^2=4^2+3^2-2(4)(3)(0.848)\\\\a^2=16+9-20.352\\\\a^2=4.648\to a=\sqrt{4.648}\\\\a\approx2.2

5 0
3 years ago
Designer Dolls found that its number of Dress-Up Dolls sold, N, varies directly with their advertising budget, A, and inversely
Radda [10]

Answer:

25,600

Step-by-step explanation:

You can use the rule of three considering that the number of dolls sold varies directly with the advertising budget:

$54,000    →   9,600

$144,000   →       x

x=\frac{144,000*9,600}{54,000}

x=25,600

According to this, the number of dolls sold if the amount of advertising budget is increased to $144,000 is 25,600.

4 0
3 years ago
Ashton walked into restaurant and 4 employees were working registers. Use the trend line equation to predict how long he will wa
Ulleksa [173]

The trend line simply means a line that's drawn over pivot to show the prevailing direction of price.

<h3>What is a trend line equation?</h3>

Your information is incomplete. Therefore, an overview will be given.

The trend line simply means a line that's drawn over pivot to show the prevailing direction of price.

It should be noted that trend lines are use for making trading decisions.

Learn more about trend line on:.

brainly.com/question/8241509

#SPJ1

5 0
2 years ago
What is -6a + a + 28a
Alisiya [41]

-6a+a+28a=-6a+29a=23a

Hope this helps.

4 0
3 years ago
Read 2 more answers
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