1. Find the area of the following triangle: c = 210 ft, A = 42.5 degrees, B = 71.4 degrees
All I know is C will be 66.1 degrees...
2. The range of a sequence is the set of positive integers.
True?
a. a neat way to get area is this relation
area=sqrt(s(s-a)(s-b)(s-c))
where s is half the perimeter, and a,b,c are the sides.
You can get the last side with the law of sines.
b. false. Consider this sequence:
-3,-2,-1, 0, 1, 2, ...
To find the area of a triangle, you will need two sides and the angle between them. In this case, you are given side c, which is 210 ft, and the angles A and B.
First, we can find angle C using the fact that the sum of angles in a triangle is always 180 degrees. Since you know angles A and B, you can use the formula:
C = 180 - A - B
C = 180 - 42.5 - 71.4
C = 66.1 degrees
Now that you have all three angles, you can use the Law of Sines to find the lengths of the remaining two sides, a and b:
a/Sin(A) = c/Sin(C)
a/Sin(42.5) = 210/Sin(66.1)
To find a, multiply both sides by Sin(42.5):
a = 210 * Sin(42.5) / Sin(66.1)
Similarly, you can find b using the formula:
b/Sin(B) = c/Sin(C)
b/Sin(71.4) = 210/Sin(66.1)
To find b, multiply both sides by Sin(71.4):
b = 210 * Sin(71.4) / Sin(66.1)
Now that you know all three sides, you can use Heron's formula to find the area of the triangle:
Area = sqrt(s(s - a)(s - b)(s - c))
where s is the semiperimeter (half of the perimeter):
s = (a + b + c) / 2
Substituting the values of a, b, and c, you can calculate the area of the triangle.