Question

The Capilano Suspension Bridge to North Vancouver is the world’s highest footbridge of its kind. The bridge is 140m long. From the ends of the bridge, the angles of depression of a point on the river under the bridge are 41 degrees and 48 degrees. How high is the bridge above the river to the nearest metre?

Answer 1

see the attached picture to better understand the problem

we know that
in the right triangle ABC
tan 48=AC/AB--------> AC=AB*tan 48-----> AC=x*tan 48-----> equation 1

in the right triangle ACD
tan 41=AC/AD-----> AC=AD*tan 41------> AC=(140-x)*tan 41----> equation 2

equate equation 1 and equation 2

x*tan 48=(140-x)*tan 41----> x*tan 48=140*tan 41-x*tan 41
x*[tan 48+tan 41]=140*tan 41
x=140*tan 41/[tan 48+tan 41]-----> x=61.468 m

find AC
AC=x*tan 48-----> AC=61.468*tan 48----> AC=68.27 m----> AC=68 m

the answer is
68 m