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Nitella [24]
3 years ago
7

What is the height of the triangle? A) 17 units B) 34units C) 51units D) 68units Help??

Mathematics
1 answer:
drek231 [11]3 years ago
8 0

Answer:

51 units

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

short leg : long leg : hypotenuse = 1 : sqrt(3) : 2

The reason this is relevant here is that in your case, you start with an equilateral triangle, FGH. An equilateral triangle is also equiangular, so all angles are congruent and measure 60 deg.

m<F = m<FGH = m<H = 60 deg

When the height GR is drawn, <FGH is bisected creating two 30-60-90 degree triangles, FGR and HGR.

The altitude GR also bisects side HF, so

HR = FR = (1/2)HF = 17*sqrt(3)

In 30-60-90 degree triangle FRG, the short leg is FR; the long leg is GR; the hypotenuse is FG.

Now we use the ratio of the lengths of the sides of a 30-60-90 degree triangle.

short leg : long leg : hypotenuse = 1 : sqrt(3) : 2

We use only the short leg and long leg parts of the ratios.

17*sqrt(3) : GR = 1 : sqrt(3)

GR * 1 = 17 * sqrt(3) * sqrt(3)

GR = 17 * 3

GR = 51

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3 years ago
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Step-by-step explanation:

Step 1; Rachel learns for 45 minutes a day from Monday through Friday and in the weekend she learns to play the violin for one and a half hours. So she learns for the following periods of time

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Tuesday - 45 minutes

Wednesday - 45 minutes

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Sunday - 90 minutes (60 × 1.5 hours)

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2 years ago
For a school play, 739 tickets valued at $857 were sold. Some cost $1 and others cost a $1.50. How many $1 tickets were sold?
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Answer:

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Step-by-step explanation:

Use two equations  

Let x = number of $1 tickets sold  

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Plug this into the second equation  

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