A soap box derby is a contest in which the cars competing rely only on gravity to move. There is nothing motorized in the car. These gravity racers are typically either pushed by others at the start of a race or the race is downhill. DeMarius is constructing a car to enter into a soap box derby. The side panel of the car is shown.
1. What is the length of the side of the side panel opposite the obtuse angle? Round your answer to the nearest hundredth.
2. What is the area of the side panel? Round your answer to the nearest hundredth.
3. On the side of the panel, a bright yellow triangle is painted whose sides measure 2 feet, 3.5 feet, and 5 feet. What is the area of the bright yellow triangle? Round your answer to the nearest hundredth.
+23246 1) Using the Law of Sines to find the length of the side opposite the 130o angle:
Find the size of the third angle: 180o - 130o - 19o = 31o.
side / sin(130) = 7 / sin(31) ---> side = 7 / sin(31) x sin(130) = 10.41
2) Area = ½ · a · b · sin(C) ---> Area = ½ · 7 · 10.41 · sin(19) = 11.9
3) Heron's formula: Area = sqrt[ s · (s - a) · (s - b) · (s - c) ]
s = ( a + b + c ) / 2 ---> s = (2 + 3.5 + 5 ) / 2 ---> s = 5.25
Area = sqrt[ 5.25 · (5.25 - 2) · (5.25 - 3.5) · (5.25 - 5) ] = 2.73
