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sladkih [1.3K]
3 years ago
11

Three lines of crops in a garden form a triangular shape. Strawberries are planted in a 10 ft line and green beans are planted i

n an 18 ft line. If the third side, a line of pumpkins, makes an 68 degree angle with the strawberries, determine the length of the pumpkins.
Mathematics
1 answer:
Marat540 [252]3 years ago
6 0

Answer:

p = 19.18

Step-by-step explanation:

This question is illustrated using the attachment and will be solved using cosine formula

a^2 = b^2 + c^2 - 2bcCosA

<em>Let the strawberry side be s, the Green beans be b and the pumpkins be p.</em>

<em />

The cosine formula in this case is:

g^2 = s^2 + p^2 - 2spCosG

Where

s = 10

g = 18

The equation becomes

18^2 = 10^2 + p^2 - 2 * 10 * p * Cos\ 68

324 = 100 + p^2 - 20 * p * 0.375

324 = 100 + p^2 - 7.5p

Collect Like Terms

p^2 - 7.5p + 100 - 324 = 0

p^2 - 7.5p - 224 = 0

Using quadratic formula:

p = \frac{-b\±\sqrt{b^2-4ac}}{2a}

Where

a = 1

b = -7.5

c = -224

p = \frac{-(-7.5)\±\sqrt{(-7.5)^2-4*1*-224}}{2*1}

p = \frac{7.5\±\sqrt{56.25+896}}{2}

p = \frac{7.5\±\sqrt{952.25}}{2}

p = \frac{7.5\± 30.86}{2}

p = \frac{7.5 + 30.86}{2} or p = \frac{7.5 - 30.86}{2}

p = \frac{38.36}{2} or p = \frac{-23.36}{2}

p = 19.18 or p = -11.68

But length can not be negative.

So:

p = 19.18

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