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Shalnov [3]
3 years ago
6

What is the length of this line? 30 POINTS!!

Mathematics
2 answers:
stepan [7]3 years ago
6 0

Distance formula: d =√(x2-x1^2 +y2-y1^2)

Find the points of the line: (2,2) and (8, 7)

Length = √((8-2)^2 + (7-2)^2)

Length = √(6^2 + 5^2)

Length = √(36+25)

Length = √61 ( exact answer) or as a decimal: 7.81

Novay_Z [31]3 years ago
3 0

Answer:

61

Step-by-step explanation:

The first thing that you want to do is distance formula

d=(x_{2}-x_{1} )^{2} + (y_{2}-y_{1} )^{2}

I'm going to make the start of the line at (1,1) and that means that the end of the line is at (7,6). Now, you plug these numbers into the formula.

d=(7-1 )^{2} + (6-1 )^{2}

Then you slove

d=(6 )^{2} + (5 )^{2

d=36 + 25

d=61

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6) Two coastguard stations P and Q are 17km apart, with due East of P. A ship S is observed in distress on a bearing 048° fromP
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The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.

Step-by-step explanation:

Let the distance of the ship to coastguard P be represented by x, and its distance to coastguard Q be represented by y.

But,

<P = 048°

<Q = 360^{o} - 324^{o}

     = 036^{o}

Sum of angles in a triangle = 180^{o}

<P + <Q + <S = 180^{o}

048° + 036^{o} + <S = 180^{o}

84^{o} + <S = 180^{o}

<S  = 180^{o} -  84^{o}

    = 96^{o}

<S = 96^{o}

Applying the Sine rule,

\frac{y}{Sin P} = \frac{x}{Sin Q} = \frac{z}{Sin S}

\frac{y}{Sin P} = \frac{z}{Sin S}

\frac{y}{Sin 48^{o} } = \frac{17}{Sin 96^{o} }

\frac{y}{0.74314} = \frac{17}{0.99452}

⇒ y = \frac{12.63338}{0.99452}

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y = 12.70 km

\frac{x}{Sin Q} = \frac{z}{Sin S}

\frac{x}{Sin 36^{o} } = \frac{17}{Sin 96^{o} }

\frac{x}{0.58779} = \frac{17}{0.99452}

⇒ x = \frac{9.992430}{0.99452}

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x = 10.05 km

Thus,

the ship S is at a distance of 10.05 km to coastguard P, and 12.70 km to coastguard Q.

6 0
3 years ago
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