Question

Remy stands on a dock at the edge of the lake represented by point C. Points A and B represent two buoys anchored in the lake. Remy plans to swim from C to A, then to B and then back to C. The shortest distance from Remy to the swim route AB is 60 meters and is measured from C to D.

What is the total distance, in Meters that Remy will swim? Round your number to the nearest whole number.

Answer 1

*see attachment for the diagram and more info

Answer:

236 m

Explanation:

Total distance Remy will swim = CA + AD + DB + BC

✔️Find AD and CA using trigonometry function:

Reference angle = 43°

Opp = AD

Hypotenuse = CA

Adjacent = 60 m

Tan 43 = opp/adj

Tan 43 = AD/60

60 × Tan 43 = AD

60 × 0.93 = AD

55.8 = AD

✅AD = 55.8 m

Cos 43 = adj/hyp

Cos 43 = 60/CA

CA × Cos 43 = 60

CA = 60/Cos 43

CA = 60/0.73

✅CA ≈ 82.2 m

✔️Find DB and BC:

Refernece angle = 27°

Adj = 60 m

Opp = DB

hyp = BC

Tan 27 = opp/adj

Tan 27 = DB/60

60 × Tan 27 = DB

60 × 0.51 = DB

✅DB = 30.6 m

Cos 27 = adj/hyp

Cos 27 = 60/BC

BC = 60/Cos 27

BC = 60/0.89

✅BC ≈ 67.4 m

✔️Total distance Rent will swim = 55.8 + 82.2 + 30.6 + 67.4 = 236 m