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mathsux

Member

Registered: 2007-08-06

Posts: 10

Further Trig: Bearings Question

i'm having trouble both understanding the question and drawing up a diagram.

Key: 026T = 26 Degrees True North

From point A, a lighthouse is on a bearing of 026T and the top of the lighthouse is at an angle of elevation of 12 degrees. From a point B, the lighthouse is on a bearing of 296T and the top of the lighthouse is at angle of elevation of 14 degrees. If A and B are 500 metres apart, find the height of the lighthouse, to the nearest metre. (Metric Metre)

Pleeeeeeaaase help!

mathsux

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Further Trig: Bearings Question

We know that

(alternate angles)

Also,

(alternate angles)

(complementary angles)

Hence,

Next, letting we express x and y in terms of the height:

Now since we have LA and LB, and we know ALB is right angled, we simply use pythagoras to solve for h:

The answer is 80.88m. (The answers are wrong)

Last edited by Identity (2007-08-20 01:48:18)