A lighthouse

A lighthouse overlooks a bay, and it is 77 meters high. From the top, the lighthouse keeper can see a yacht southward at an angle of depression of 32 degrees and another boat eastward at an angle of 25 degrees. What is the distance between the boats?

Correct answer:

x =  206 m

Step-by-step explanation:

h=77 m α=32° rad=32° 180π =32° 1803.1415926 =0.55851=8π/45 β=25° rad=25° 180π =25° 1803.1415926 =0.43633=5π/36   tan α = h:a = h/a  a=h/tanα=77/tan0.5585123.2258 m   tan β = h:b = h/b  b=h/tanβ=77/tan0.4363165.127 m  x2 = a2+b2  x=a2+b2=123.22582+165.1272=206 m

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