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blondinia [14]
3 years ago
6

Find the height of a triangle with area 85 1/3 ft squared and base 10 2/3 feet squared

Mathematics
1 answer:
schepotkina [342]3 years ago
5 0
Lets convert the fractions first:
85 1/3 = 255/3 + 1/3 = 256/3
10 2/3 = 30/3 + 2/3 = 32/3
now, the equation to find the area of a triangle is:
area = height*base/2
so the height is:
height = 2*area/base
then we substitute:
height = 2*(256/3)/(32/3)
= <span>(2*256/3)/(32/3)
</span><span>= (512/3)/(32/3)
</span>now, dividing by a fraction is the same as multiplying by that fraction upside down:
= <span>(512/3)(3/32)
</span>= (512*3)/(3*32)
= 1536/96
= 16
therefore the height of the triangle is 16 ft
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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.

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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.

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<P = 048°

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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}

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\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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