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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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At Niagra High, Mr. Borton bought 4 student tickets and 2 adult tickets for the high school musical which cost $64. then Mrs. Ge
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Answer:

Each student ticket costs $8.33

Each adult ticket costs $15.34

Step-by-step explanation:

At Niagra High, Mr. Borton bought 4 student tickets and 2 adult tickets for the high school musical which cost $64. then Mrs. Gelvoria bought 3 student tickets and 3 adult tickets for the show and it cost her $72. How much are each type of tickets?​

s = cost of each student ticket

a = cost of adult ticket

Our system of equations:

4s + 2a = 64

3s + 3a = 71

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2(3s + 3a = 71) ==>     6s + 6a = 142

-12s - 6a = -192

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/-6      /-6

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Now, let's find the cost of each adult ticket:

4s + 2a = 64

4(8.33) + 2a = 64

33.32 + 2a = 64

-33.32         -33.32

2a = 30.68

/2        /2

a = 15.34 (the cost of each adult ticket)

(x, y) ==> (8.33, 15.34)

Check your answer:

4s + 2a = 64

4(8.33) + 2(15.34) = 64

33.32 + 30.68 = 64

64 = 64

This statement is true

Hope this helps!

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