Draw a "side view"
Draw 3 points on the river, B , C, and D , B to the left of the points
draw a point A above B so that angle B is 90°
Join AC and AC , so that CD = 20
Mark angle ADC = 62.6° and angle ACB = 72.8°
label AB =h (h is the height) , BC = x
in triangle ABC:
tan 72.8° = h/x
h = xtan72.8°
in triangle ABD
tan62.6° = h/(x+20)
h = (x+20)tan62.6°
xtan72.8 = (x+20)tan62.6
xtan72.8 - xtan62.6) = 20tan62.6
x(tan72.8 - tan62.6) = 20tan62.6
x = 20tan62.6/(tan72.8 - tan62.6)
sub back into h = xtan72.8
h = 20(tan62.6)(tan72.8)/(tan72.8-tan62.6)
= ..... you do the button pushing
notice up to this point, I have not done any arithmetic or calculator work.
Also notice that the fact that the bridge was 1 km long did not enter the picture. It is important that you recognize what information is relevant and what is not.
BTW, I got 95.79 m
in triangle ACD (not right-angled) , angle A = 10.2° , angle C = 107.2°
By the Sine Law:
AC/sin62.6 = 20/sin10.2
AC = 20sin62.5/sin10.2
in the right-angled triangle ABC
sin72.8 = h/AC
h = AC sin72.8 = (20sin62.6/sin10.2)(sin72.8) = 95.79
HOW ABOUT THAT ??
Thanks so much!
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