How do you solve this question: h= (d*sinA*sinB)/(sin(B-A)?

A man at sea is rowing his boat towards the lighthouse.
From a certain point, he finds the angle of elevation of the top of the lighthouse is A.
After rowing a further distance d meters towards the lighthouse he finds that the angle of elevation of its top is B.
if h is the height figure out the asked question.
you may need to draw a diagram to help you.

1 Answer
Noah G
Apr 14, 2018

Always draw a diagram.
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We start by determining the angle directly to the left of B. This will be simply #180 - B#.

In order to apply sine law to determine the blue side, we will have to determine the measure of the angle opposite side of length #d#. This will be given by

#180 - A - (180 - B) = 180 - A - 180 + B = B - A#

Now use the law of sines to determine the blue side

#(sin(B - a))/d = sinA/("blue")#

And we know that #sinB = h/"blue"#. Therefore #"blue" = h/sinB#.

#(sin(B - A))/d = sinA/(h/sinB)#

#(sin(B - A))/d = (sinAsinB)/h#

#h = (dsinAsinB)/(sin(B - A))#

As required.

Hopefully this helps!

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