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soldier1979 [14.2K]
2 years ago
9

Solve the triangle. Round your answers to the nearest tenth.

Mathematics
1 answer:
Tresset [83]2 years ago
6 0

Answer:

<B = 47°

<C = 28°

b = AC = 28.0

Step-by-step explanation:

Given:

∆ABC

AB = c = 18

BC = a = 37

<A = 105°

Required:

Length of AC = b

measure of angle B and angle C

SOLUTION:

==>Use the sine rule, sin A/a = sinC/c to find the angle of C:

SinA = sin(105) = 0.9659

a = 37

sinC = ?

c = 18

0.9659/37 = sinC/18

Cross multiply

0.9659*18 = 37*sinC

17.3862 = 37*sinC

Divide both sides by 37

17.3862/37 = sinC

0.4699 = sinC

sinC = 0.4699

C = Sin-¹(0.4699)

C = 28.0° (nearest tenth)

==>Find angle B using sum of angles in a triangle:

Angle B = 180 - (105+28)

Angle B = 180 - 133

Angle B = 47°

==>Find length of b using sine rule, b/sinB = c/sinC:

SinC = sin(28) = 0.4695

SinB = sin(47) = 0.7314

c = 18

b = ?

b/0.7314 = 18/0.4695

Cross multiply

b*0.4695 = 18*0.7314

b*0.4695 = 13.1652

Divide both sides by 0.4695

b = 13.1652/0.4695

b = 28.0 (nearest tenth)

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Answer:

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Step-by-step explanation:

60ft x 60ft = 3600 square feet

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2 years ago
Jensen has an above ground pool in the shape of a regular octagon. Opposite sides are 25 feet apart and each side is 10.4 feet l
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Answer:

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Now, 1 cubic ft takes 7.5 gallons to fill.

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6 0
3 years ago
900% of it is 450 ?<br><br> please help with this
charle [14.2K]
900% of 450=4050

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 450 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 450 is 100%, so we can write it down as 450=100%.
4. We know, that x is 900% of the output value, so we can write it down as x=900%.
5. Now we have two simple equations:
1) 450=100%
2) x=900%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
450/x=100%/900%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 900% of 450

450/x=100/900
(450/x)*x=(100/900)*x - we multiply both sides of the equation by x
450=0.111111111111*x - we divide both sides of the equation by (0.111111111111) to get x
450/0.111111111111=x
4050=x


now
4 0
3 years ago
Amber is 48 inches tall and her friend Lucy is 60 inches tall. In a photograph of them together, Amber is 3 inches tall. Which p
irina [24]
The answer would be the Last option (D). This because it poses the proportion of 48 in (Amber's height) / 60 in (Lucy's height) and puts it equal to the proportion of x (what is Amber's height in the photo) / 3 (what is Lucy's height in the photo. Hope this helps :)
4 0
3 years ago
There were 240 students at a primary school. After some new students were transferred into the school, there were 282 students i
stepan [7]

Answer:

Numbers of students at a primary school before= 240

Number of increased students =42

Again,

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Therefore 17.5% students are increased this year.

3 0
3 years ago
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