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# A swamp separates points L and R.

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A swamp separates points L and R. To determine the distance between them, Ciana stands at L and looks toward R. She turns about 45° and walks 52 paces from L to point P. From P, she looks at R and estimates that LPR is about 60°. How many paces is it from L to R?
Include a diagram.

An observation helicopter using a laser device determines that the helicopter is 1800 m from a boat in distress. The helicopter is 1200 m from a rescue boat. The angle formed between the helicopter and the two boats is 35°. How far apart are the boats? Include a diagram.

Jun 9, 2019
edited by Guest  Jun 9, 2019

#1
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P

60

52

L   45                75  R

Angle  LRP  =  180 - 60 - 45  =  180 - 105  =  75°

Using the Law of Sines, we have that

52/sin(75°) = LR / sin(60°)

LR  =  52*sin(60°) /sin (75°)  ≈  47 paces   Jun 9, 2019
#2
+1

Helicopter

35°

1200m                                              1800

Rescue Boat                    D                                  Distressed Boat

We  can use the Law of Cosines herer

D^2  =  1200^2 + 1800^2  - 2(1200)(1800)cos(35°)

D   =  sqrt [ 1200^2 + 1800^2 - 2(1200)(1800) cos (35°) ] =   1068 m   Jun 9, 2019