Math problem?

Question

From the top of a light house, the angles of deppression of two ships on the opposite sides of the light house are observed as 60and 45 degrees. if the height is 200m, find the dist between the ships.

Answer 1

Tanθ = y / x

tan60 = 200 / x

xtan60 = x(200 / x)

x tan60 = 200

x tan 60 / tan60 = 200 / tan60

x = 200 /tan60

x = 200 / 1.732050808

x = 115.4700538 m

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tanθ = y / x

tan45 = 200 / x

x tan 45 = x(200 / x)

x tan 45 = 200

x tan 45 / tan 45 = 200 / tan45

x = 200 tan45

x = 200 / 1

x = 200 m

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The distance between the ships

200 + 115.47 = 315.47 m

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Answer 2

the hight of the light house = T
let name them S1 and S2 (ship 1 and ship 2)
for the first one at angle 45 and distance from the lighthouse to S1 = Y
Tan 45 = Y / T (trigeometrics) Tan 45 =1
1 = Y / 200 so Y = 200m

for the 2nd one at angle 60 and distance from the lighthouse to S2 = X
Tan 60 = X / T (trigeometrics) Tan 60 =1.732
1.732 = Y / 200 so X = 200 * 1.732
So X = 346.41

the distance between the two ships is X + Y
= 346.41 + 200 = 546.41m

hope I helped

Answer 3

You don't want the answer, you should work that out yourself, its a basic trigonometry question, get some paper a rule and a protractor and draw it. Yo say the lighthouse is 200M, is that above sea-level?, the ships distance, if you want to be a perfectionist has to take account of the earths curvature, but i don't think you have to worry about that. The way i work these things out now is by the use of CAD. Most schools and colleges have this software, you could draw and it in real-time and the calculations would be done in under a minuet. Being a maths question get that paper and draw it. Edx

Answer 4

The answer is 2

Answer 5

90 yards

Answer 6

Wow...kudos to those who will actually help with that complicated question.