jugoslav

This is too easy!!! 

ON = 1/3(QN)                (Median theorem)

NR = 1/2(PR)

OR = sqrt[(ON)² + (PR)²] 

ΔABC ~ ΔACD        BD = CD = 2          ∠B = ∠CAB =  β  

CD / AC = AC / BC

2 * 4 = (AC)²

AC = √8

sinβ / 2 = sin49 / √8

Angle B ≈ 32.253º

D is on side BC of triangle ABC. We know ABC ~ ACD and angle A = 49 degrees.  If BD = CD, what is angle B in degrees? 

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After a small correction, this becomes a very challenging question.

Let ABCDEFGH be a rectangular prism, where EF = 4, EH = 15 (?), and EA = 6. Find the volume of pyramid CFAH.

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Prism volume = (EF)(EH)(EA) = 360 u³

There are 5 pyramids of which 4 have a volume of 60 u³ each.

The volume of pyramid CFAH = 360 - (4 * 60) = 120 u³

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If EH = 5 then the volume of a pyramid CFAH = 40 u³

A right triangle has legs of length  6 and b, and a hypotenuse of length c.                                                                      The perimeter of the triangle is 15. Compute c.

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a = 6             b + c = 9           b = 9 - c           P = 15

a² + b² = c²

6² + (9 - c)² = c²

c = 6.5                (b = 2.5)

I'm not Phill or Melody, but I think that I can help you. 

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First, I'm gonna correct your question:

"The total length of the lines she draws is 180 cm."     (NOT 18 cm)

On the second piece of paper, Pat drew only 4 lines, and each line was 18 cm long. 

Hi, Techno! You misunderstood the question.

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A rectangular box has integer side length in the ratio 1:3:4. Which of 48, 56, 64, 96, 144 could be the volume of the box?

1 : 3 : 4 = 2 : 6 : 8 = 3 : 9 : 12

1 * 3 * 4 = 24    

2 * 6 * 8 = 96   Only the volume of 96 u<sup>3</sup> is possible with the given integer side length ratio!!!

3 * 9 * 12 = 324

BD = 8*sin(37º)

Angle X = sin<sup>-1</sup>(BD / 11)

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