A lighthouse with a rotating beam is located 500m south of a coastal cliff that runs west to east

Question

a) determine a relation for the distance from the lighthouse to the point the light strikes the cliff in terms of the angle of rotation x

b) determine an exact expression for this distance x = 5pi/12

I have the answer for a) worked out, which is secx(500) = d, but I do not now how to do b). The answer for b) is d=100sqrt.2/sqrt.3 - 1

Answer 1

note that 5π/12 = 2π/3 - π/4

Now just use your difference formula for cos(a-b) and take the reciprocal for sec(x)

Answer 2

thankyou so much! i got the answer with some prompting :)