# 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.