(a) One unique triangle. This is an equilateral triangle since all sides are the same length. Through the SSS property, we can prove that only one triangle is possible here.
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(b) Cannot make a triangle. The triangle inequality theorem says that adding any two sides of a triangle must result in a value larger than the third side. Add up the first two sides (1 and 2) to get 1+2 = 3, which is not larger than the third side (3 units long). I recommend cutting out strips of paper that are 1 inch, 2 inches and 3 inches long, and trying to form a triangle. You'll find that a triangle is not possible. The 1 inch and 2 inch strips will line up to form a straight line that is 3 inches long, and basically you have a flat line (or a triangle with area 0)
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(c) More than one triangle. The angles add up to 180 since 35+60+85, so we can form a triangle. It turns out we can form infinitely many of them. The AA (angle angle) similarity theorem allows us to scale any triangle to make it larger or smaller compared to the original.
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(d) Cannot make a triangle. I'm assuming the 509 should actually be 50°. If so, then a triangle is not possible because the three angles (50, 50, 50) do not add to 180. We have instead 50+50+50 = 150. For any triangle, the three angles must always add to 180 degrees.
Answer:
AC is about 41. 095 miles long.
Step-by-step explanation:
You can use the Law of Cosines to solve this: c^2 = a^2 + b^2 – 2ab cos(C)
Substitute in your values, and you're good to go!
c^2=16^2+28^2-2(16)(28)(cos(117))
c^2 = 256 + 784 - 896(cos(117))
c = sqrt(1040 - 896(cos(117)))
c is about 41. 095 miles long.
C. 27,384 is the answer.
A. 26,413 rounds to 26,400
B. 27,345 rounds to 27,300
D. 27,499 rounds to 27,500
Step-by-step explanation:
<u>Substitute the given value of x into the expression;</u>
<u />
<u>Multiply;</u>
<u />
<u>Subtract;</u>
<u />
Answer:
just look at the 10 years in the past then we produce more people then we lose so times it by 3
