Answer:
Step-by-step explanation:
1)
we are given ∠17 and the Adj = 200 meters they want to know the Opp
so use TOA
Tan(17) = Opp / 200
200*Tan(17) = Opp
61.146 = Opp
the mast stands 61.1 meters tall ( rounded to nearest 10th )
2)
now we know the opp = 40 meters and the angle is 35° and Adj = x
Use TOA again, but w/ the different knowns
Tan(35) = 40 / Adj
Adj = 40 / Tan(35)
57.1259 = Adj
so the boat is 57.1 meters from the cliff ( rounded to nearest 10th)
3)
we are given two triangles now and are told to find the difference between them to find the distance between the buoys
Opp = 70
∠A = 60
∠B = 40
we want to find the Adj for each so use TOA
for A , then
Tan(60)= 70/a
a = 70 / Tan(60)
a = 40.4145
for B, then
Tan(40) = 70 /b
b = 70 / Tan(40)
b = 83.4227
so subtract a from b
83.4227 - 40.4145 = 43.008
so from buoy A to buoy B is 43.0 meters ( rounded to nearest 10th )
:)
