Answer:
Step-by-step explanation:
Use SOH CAH TOA to recall how the trig functions fit on a triangle
SOH: Sin(Ф)= Opp / Hyp
CAH: Cos(Ф)= Adj / Hyp
TOA: Tan(Ф) = Opp / Adj
we can find angle C b/c the angles of a triangle always add to 180 , soo
180= C + 81 +63.5
35.5 = C
now that we have angle C and we know the Hyp we can use sin to find side g
where g = Opp and Hpy = 13.8 for this question
Sin(35.5) = Opp / 13.8
13.8*Sin(35.5) = Opp
8.0137 = Opp
g = 8.0137
next they ask for the area of the biggest triangle ABC ( there are two smaller ones when you use D )
we can use 1/2 * base * height , but we don't know the base yet, even thou we do know the height.
we can solve for line segment CD and DB and then add them for the side a .. or the base of the biggest triangle sooo.. CD = adj
Cos(35.5) = Adj / 13.8
13.8*Cos(35.5) = Adj
11.234794 =Adj
now solve for DB using cos again but with the other smaller triangle where Adj = DB now
Cos(63.5) = Adj / 8.9
8.9*Cos(63.5) = Adj
3.971160
add these two Adjs together to get the total 'a' side
15.205954
now plug in side a as the base and g as the height of our biggest triangle
Area = 1/2 * 15.205954 * 8.0137
Area = 60.9159
rounded to 2 sig figs
Area = 60.92 :) hope you get an "A" :P
