Q1:
The High Level Bridge,a railway bridge that crosses the Oldman River,is over 1 km long.From one point A on the river,the angle of elevation of the top of the bridge is 62.6 degrees.From a point 20 m closer to the brdige,the angle of elevation of the top of the bridge is 72.8 degrees.How high is the bridge above the river,to the nearest metre?
Solution:
Let the height of bridge above the river be h.
Let the orizontal dinstance between bridge and the first point A be x.
tan 62.6°= H/x,x = H/tan 62.6°
tan 72.8°= H/(x-20),x = 20 + H/tan 72.8°
So,H/tan 62.6°= 20 + H/tan 72.8°
H(1/tan 62.6°- 1/tan 72.8°) = 20
H = 20/(1/tan 62.6°- 1/tan 72.8°) ≈ 96 (m)
Q2:
Hobbyists often compete with their model rockets to determine which rocket flies the highest.On one test launch,a rocket was fired vertically upward.The angle of elevation to the top of the flight was measured from two points that were 20 m apart,on the same side of the launch site,and collinear with it.The angles measured a the two points were 66 degrees and 37 degrees.How high did the rocket fly,to the nearest metre?
Solution:
Similarly to question 1:
H = 20/(1/tan 37°- 1/tan 66°) ≈ 23 (m)