For the right-angled triangle △MPQ the tangent of the angle of elevation at point M is ⇒tan45∘=PQ∕PM=
50+h
100
where h is the additional height at point Q due to the smoke Since tan45∘=1 ⇒1=
50+h
100
=100=50+h ⇒h=50m So, the height at point Q due to the smoke is 50 meters. Finding the angle ∠RMQ ∠RMQ, is formed by the line PR (the straight line from P to R ) and the line PM . Using the definition of the tangent function, we have ⇒tan∠RMQ=