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aalyn [17]
2 years ago
9

Find the diagonal BD simplify you answer (Explain)

Mathematics
1 answer:
Dima020 [189]2 years ago
5 0

Answer:

See below:

Step-by-step explanation:

First of all, you will see that diagonal BD is a angle bisector for Angles <ABC and <ADC. Now, knowing that it is a square.

We see that the angle bisector splits the angles into 45 degrees each due to the sum of angles in a square being 360 degrees hence giving us 4 right angles.

Now, if we see this, we see that we have a 45 45 90 Triangle!

The theorem states that the hypotenuse is equal to x\sqrt{2}.

Hence, we get our answer of 5\sqrt{2}!

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I need help with finding the least number that 12 14 and 16 go into equally
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1 or 2

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Write down the numbers that go into each one

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Factor the trinomial or state that the trinomial is prime 3a^2 -10a-32
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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<span>)
</span>
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

8 0
3 years ago
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