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Reil [10]
3 years ago
5

What is the length of BC¯¯¯¯¯ ?

Mathematics
1 answer:
svlad2 [7]3 years ago
5 0

Hello!


The length of side BC can be found by using the Law of Sines. This law states,

a / sin A = b / sin B = c / sin C.


Given:

Angle A = 51.2 degrees

Angle B = 60.3 degrees

Side AC (or B) = 21 cm

Side BC (or A) = ? cm


Let's plug in these values into the formula to find the missing side length.


a / sin (51.2) = 21 / sin (60.3)

a / sin (51.2) = 24.1759... (multiply both sides by sin(51.2)

a = 24.1759 · sin (51.2)

a = 18.841...


18.841 can be rounded to 19.


Therefore, the length of side BC is equal to 19 centimeters.

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Triangle rst is dilated by a scale factor of 5 to form triangle r's't'. side r's' measures 40. what is the measure of side rs?
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1 year ago
Molly is painting a model house and needs to know how much paint she will need. She knows the surface area of the prism is 216 s
mrs_skeptik [129]

Answer:

1. Base of pyramid; 6 in by 6 in

2. Base of prism; Its dimensions are also 6 in by 6 in, located at the bottom of the house and will not be seen, so it does not require painting.

3. twice the area of the square

4. Area = 228 inches squared

Step-by-step explanation:

For question 4, the area Molly needs to paint is found by adding all the surface areas and subtracting the 2 surfaces that will not be painted: base of pyramid and base of prism (outlined in red). According to the picture, these are both squares with 6 by 6 dimensions.

<h3>Step 1. Add all surface areas together</h3>

Prism: 6 surfaces

Surface area = 216 inches sq

  • Front = 6 x 6 = 36
  • Back = 6 x 6 = 36
  • Top = 6 x 6 = 36
  • Bottom (base) = 6 x 6 = 36
  • Side = 6 x 6 = 36
  • Other side = 6 x 6 = 36

Pyramid: 5 surfaces

Surface area = 84 inches sq

  • Bottom (base) = 6 x 6 = 36
  • Front triangle = (6 x 4)/2 = 12
  • Back = (6 x 4)/2 = 12
  • Side = (6 x 4)/2 = 12
  • Other side = (6 x 4)/2 = 12

TOTAL surface area: 216 inches + 84 inches = 300 inches sq

<h3>Step 2. Subtract surfaces that are NOT being painted</h3>

300 - base of pyramid - base of prism

300 - 2(36)

300 - 72

<u>228 inches sq</u>

Hope this helps!

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