Answer:
156.06 ft²
Step-by-step explanation:
The applicable formula for the area of the triangle is ...
Area = (1/2)bc·sin(A)
Filling in the given numbers, you have ...
Area = (1/2)(30 ft)(14 ft)·sin(48°) ≈ 156.06041335 ft²
The area of the triangle is about 156.06 square feet.
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Sufficient digits are provided here so that you can round to the precision you (or your computer) may desire.
Wording is everything. Here, there are some issues. "... at the rate of 1/2 per month" can be interpreted to mean that at the end of the first month, there are 649 1/2 items in Marie's closet (decreased by 1/2 from 650).
"The number of items Dustin adds" could mean 5 items, the number he adds each month. The wording should specify the time period or whether we're talking about the total number Dustin has added.
We assume your description means that the number of items in Marie's closet at the end of each month is 1/2 what it was at the beginning. (As opposed to decreasing by 1/2 item each month.) We assume we're interested in the total number of items of Dustin's that are in the closet.
Marie's quantity can be modeled by ...
... m = 650·(1/2)^t . . . . . t = time in months
Dustin's quantity can be modeled by ...
... d = 5t
There will be one solution for d=m, at about t = 4.8. At that point, Dustin will have added about 24 items, which will be the number Marie is down to.
There is a viable solution for d=m at about t = 4.8.
