Question

A bridge is 140m long.From the ends of the bridge, the angles of depression of a point on the river under the bridge is 41° and 48°. How high is the bridge above the river to the nearest meter. ( I know the answer is 68m, I just need to know how to get that, please explain as you go. Thank you)

Answer 1

make a sketch.
label the ends of the bridge A and B
make angle A = 41° and angle B = 48°.
label the point on the river P and Q on AB so that PQ is at right angles to AB. Let PQ = h

let QB = x , the AQ = 140-x

tan41 = h/(140-x)
h = (140-x)tan41

tan48 = h/x
h = xtan48

So xtan48 = (140-x)tan41
xtan48 = 140tan41 - xtan41
xtan48 + xtan41 = 140tan41
x(tan48+ tan41) = 140tan41
x = 140tan41/(tan48+tan41)
= .....

plug x into
h = xtan48 to get your answer
(I got appr 68.3)
Don't round off intermediate answers.

Answer 2

Thank you!!