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3 years ago

Given that R is between S and T, find the measure of TS RS=6 TR=4.5 TS=?

Mathematics

1 answer:

Ber [7]3 years ago

6 0

Answer:

$\huge\boxed{TS = 10.5}$

Step-by-step explanation:

Given that:

R is a point lying on line TS

So,

TS = TR + RS

Where TR = 4.5 and RS = 6

=> TS = 4.5 + 6

=> TS = 10.5

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Which equation correctly uses the value of b to solve for a?

BigorU [14]

If the choices are the following:
tan(22.6o) = a/13
tan(22.6o) =13/a
tan(22.6o) = a/12
tan(22.6o) = 12/a
Then the equation correctly uses the value of b to solve for a is
tan(22.6o) = a/12

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3 years ago

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Find sin(a+b) if tan(a)=7/24 where a is in the third quadrant

ludmilkaskok [199]

The complete question in the attached figure

we have that
tan a=7/24 a----> III quadrant
cos b=-12/13 b----> II quadrant
sin (a+b)=?

we know that
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

step 1
find sin b
sin²b+cos²b=1------> sin²b=1-cos²b----> 1-(144/169)---> 25/169
sin b=5/13------> is positive because b belong to the II quadrant

step 2
Find sin a and cos a
tan a=7/24
tan a=sin a /cos a-------> sin a=tan a*cos a-----> sin a=(7/24)*cos a
sin a=(7/24)*cos a------> sin²a=(49/576)*cos²a-----> equation 1
sin²a=1-cos²a------> equation 2
equals 1 and 2
(49/576)*cos²a=1-cos²a---> cos²a*[1+(49/576)]=1----> cos²a*[625/576]=1
cos²a=576/625------> cos a=-24/25----> is negative because a belong to III quadrant
cos a=-24/25
sin²a=1-cos²a-----> 1-(576/625)----> sin²a=49/625
sin a=-7/25-----> is negative because a belong to III quadrant

step 3
find sin (a+b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin a=-7/25
cos a=-24/25
sin b=5/13
cos b=-12/13
so
sin (a+b)=[-7/25]*[-12/13]+[-24/25]*[5/13]----> [84/325]+[-120/325]
sin (a+b)=-36/325

the answer is
sin (a+b)=-36/325

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3 years ago

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Anna35 [415]

Answer:

11/12

Step-by-step explanation:

We need to get a common denominator of 12

2/3 *4/4 = 8/12

1/4 *3/3 = 3/12

2/3 +1/4

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3 years ago

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iVinArrow [24]

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3 years ago

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vitfil [10]

Answer:

Hi! The correct answer is 16!

Step-by-step explanation:

~Use the formula (b/2)^2 in order to create a new term to complete the square~

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