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bazaltina [42]
3 years ago
5

PLEASE EXPLAIN BECAUSE A GIRL IS COMPLETELY LOST HERE

Mathematics
2 answers:
Virty [35]3 years ago
4 0


Don't be lost. First the triangle angles add to 180 degrees so the angle opposite b, call it B, is


B = 180 - 82 - 55 = 43 degrees


We also have a=8 cm and A=55 degrees


By the Law of Sines


\dfrac{a}{\sin A} = \dfrac{b}{\sin B}


b = \dfrac{a \sin B}{\sin A}


b = \dfrac{ 8 \sin 43 }{\sin 55 } \approx 6.7 \textrm{ cm}



Afina-wow [57]3 years ago
3 0

Hello!


To find the value of b, we need to use the Law of Sines. The law states,

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


We are given these values: sin A = 55 degrees, side a = 8 cm, sin C = 82 degrees.


Since angle B is not given, we have to find it ourselves. We can find the measure of angle B by subtracting both the given angle values from 180 degrees because every triangle is equal to 180 degrees.


180 - 55 - 82 = 43 | The measure of sin B = 43 degrees.


sin (55) / 8 = sin (43) / b (multiply both sides by b)

0.10239... · b = 0.68199... (divide both sides by 0.10239...)

c = 6.6607...


The measure of side b is equal to about 6.7 centimeters.

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There is 1000cm3 of aluminum available to cast a trophy that will be in the shape of a right square pyramid. Is this enough alum
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The 1000 cubic centimeters of aluminium is enough for aluminium a trophy  that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.

Step-by-step explanation:

The given is,

                    Volume of aluminium available is 1000 cubic centimeters

                    Shape of trophy is right square pyramid

                    Trophy has a base edge of 10 cm and slant height of 13 cm

Step:1

                     Formula for volume of right square pyramid,

                                               Volume, V = a^{2}\frac{h}{3}.....................................(1)

                     Where, a - Base edge value

                                  h - Height of pyramid

                      From given,

                                        a = 10 cm

                                        h = 13 cm

                      Equation (1) becomes,

                                           = 10^{2}(\frac{13}{3}  )

                                           = (100)(4.333)

                                           = 433.33 cm^{3}

             Volume of trophy = 433.33 cubic centimeters

             Compare with the volume of available aluminium and volume of right square pyramid,                          

            Volume of available aluminium > Volume of right square pyramid

                                               1000 cm^{3} > 433.33 cm^{3}

            So, the given volume of aluminium is enough to make right square pyramid shaped trophy.

Result:

          The 1000 cubic centimeters of aluminium is enough for aluminium a trophy  that will be in the shape of a right square pyramid and has a base edge of 10 cm and a slant height of 13 cm.

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