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3 years ago

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:

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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Answer:

The ship S is at 10.05 km to coastguard P, and 12.70 km to coastguard Q.

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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 = $360^{o}$ - $324^{o}$

= 0 $36^{o}$

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

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

048° + 0 $36^{o}$ + <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 = $\frac{12.63338}{0.99452}$

= 12.703

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 = $\frac{9.992430}{0.99452}$

= 10.0475

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.

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