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USPshnik [31]
3 years ago
10

An extremely large sink hole has opened up in a field just outside of the city limits. It is difficult to measure across the sin

k hole without falling in so you use congruent triangles. You have one piece of rope that is 50 ft. long and another that is 70 ft. long. You pick a point "A" on one side of the sink hole and "B" on the other side. You tie a rope to each spot and pull the rope out diagonally back away from the sink hole so that the two ropes meet at point "C" . Then you recreate the same triangle by using the distance from line "AC" and line "BC" and creating new segments CE and CD . The distance of line "DE" is 52.2 ft. 
What is the measure of angle ACB?

*I editted it because I realized I messed up a few things whoops

Mathematics
1 answer:
abruzzese [7]3 years ago
5 0
Triangle ABC and triangle DCE are congruent, so line DE = line AB

Use the cosine rule to find angle ACB
52.2^{2}= 50^{2}+  70^{2}-(2*50*70*cos(ACB))
2724.84=7400-(7000cos(ACB))
2724.84-7400=-7000cos(ACB)
-4675.16=-7000cos(ACB)
\frac{4675.16}{7000}=cos(ACB)
Angle ACB= cos^{-1} ( \frac{4675.16}{7000})
Angle ACB = 48.1°

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Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less
Sergio039 [100]

Answer:

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Step-by-step explanation:

Let the sides the triangle be x, y and z.

From the question, the perimeter of the rectangle is 64, that is

x + y + z = 64 ...... (1)

Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)

The third side, z, is 20 less than the sum of the other two, that is

z + 20 = x + y ...... (3)

Substitute equation (3) into (1)

Then,

z + 20 + z = 64

2z +20 = 64

2z = 64 - 20

2z = 44

z = 44/2 k

z = 22

From equation (3)

z + 20 = x + y

Then, k

22 + 20 = x +y

42 = x + y

x = 42 - y ...... (4)

Substitute this into equation 2

3x = 4y

3(42-y) = 4y

126 - 3y = 4y

4y + 3y = 126

7y = 126

y = 126/7

y = 18

Substitute this into equation (4)

x = 42 - y

x = 42 - 18

x = 24

∴ x = 24, y = 18 and z = 22

Hence, the shortest side of the triangle is 18.

4 0
3 years ago
Carlos used 6 boards to build 2/3 of a front porch. How many boards will Carlos use to build the whole porch? Express your answe
antiseptic1488 [7]

Answer:

9 boards

Step-by-step explanation:

2/3 of the porch= 6 boards

so to figure out how much one third of the porch needs you find half of what it takes to fill in 2/3 of the porch and you get 3.

so 3=1/3 of the porch

then you simply do 3times 3 or 3+3+3 and you get 9

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3 years ago
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xxTIMURxx [149]

Answer:

Step-by-step explanation:

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3 0
2 years ago
Read 2 more answers
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sveta [45]

Answer:

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Step-by-step explanation:

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3 years ago
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