Problema Solution
The angle of elevation of the highest point on a bridge is 26.6 degrees. From a point 100m closer to the bridge, the angle of elevation in 71.7 degrees. How high is the bridge the the nearest tenth of a meter?
Answer provided by our tutors
x = distance from bridge at angle 71.7 deg.
x + 100 = distance from bridge at angle 26.6.
y = height of bridge.
set up 2 equations and solve for y.
tan26.6 = y / (x + 100)
y = (x + 100)tan26.6
y = xtan26.6 + 100tan26.6
and
tan71.7 = y / x
y = xtan71.7
Now, y = y:
xtan26.6 + 100tan26.6 = xtan71.7
xtan26.6 - xtan71.7 = -100tan26.6
x(tan26.6 - tan71.7) = -100tan26.6
x = -100tan26.6 / (tan26.6 - tan71.7)
x = 19.84823...
Now use this value for x with tan71.7 to find y:
tan71.7 = y / 19.84823...
y = 19.84823...(tan71.7)
y = 60.0155 Ronded value is 60.0
X rounded value is 19.8. Then:
tan71.7 = y/19.8
y = 19.8tan71.7
y = 59.8696. - rounde to 59.9 m tall.