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

Step-by-step explanation:

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

Let the strawberry side be s, the Green beans be b and the pumpkins be p.

The cosine formula in this case is:

Where

The equation becomes

Collect Like Terms

Using quadratic formula:

Where

or

or

or

But length can not be negative.

So:

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

tap for more

y

=

−

2

find the upper bound of the range.

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y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation: