Area of "My Space" Project
Nichole Snow
What is this?
Law of Cosines Triangle ABC
Let's start with Angle C. In order to find it, we must use the following equation: c^2 = a^2 + b^2 - 2(a)(b)cosC. After plugging the numbers into the equation, you get 4,734,976 = 26,569 + 4848804 - 717,852cosC. After simplifying the right side of the equation, you get -717,852cosC = -140,397. Your next step will be to divide -140,397 by -717,852 to get cosC = 0.1956. Finally, do the inverse cosine to find that Angle C equals 78.7 degrees.
Law of Sines Triangle ABC
We still have one final angle to solve for, Angle B. To do this, we can find the sum of Angles A and C (82.9 + 78.7 = 161.6) and subtract it from 180. The measure for Angle B is 18.4 degrees.
Area of Triangle ABC
After plugging in the numbers, we will get the equation A = 1/2 (2,202)(163)sin(78.7). Our first step will be to simplify the right side to get A = 1/2 (351968.1). Then, we will multiply 1/2 by 351968.1 to get 175984.05. This is the area, in feet, of triangle ABC.
Law of Cosines Triangle BCD
To find the measure of Angle D, we will use the following equation: 2,202^2 = 2,133^2 + 1,014^2 - 2(2,133)(1,014)cos(D). After simplifying both sides, you get 4848804 = 5577885-4325724cosD. Next, subtract 5577885 from 4848804 to get -729081 = -4325724cosD. Then, divide -729081 by -4325724 to get cosD = 0.1685. Finally, do the inverse cosine of 0.1685 to get the measure of Angle D. Angle D is approximately 80.3 degrees.
Law of Sines Triangle BCD
After plugging our numbers into the formula, we get the equation sin(80.3)/2,202 = sin(C)/1,014. Our next step is to cross multiply to get 1,014sin(80.3) = 2,202sin(C). Then we simplify the left side to get 999.5 = 2,202sin(C). After this we will divide 999.5 by 2,202 to get sin(C) = 0.4539. Finally, we will do the inverse sine of 0.4539 to get 27 degrees.
Now that we know the measures of Angles D and C, we must now find the measure of Angle B. To do this, we can find the sum of Angles D and C and subtract this total from 180. After doing this, the measure of Angle B comes to 72.7 degrees.
Area of Triangle BCD
Our first step will be to simplify the right side to get A = 1/2 (2131940.6). Then we will multiply 1/2 by 2131940.6 to get 1065970.3. This is the area, in feet, of triangle BCD.