Trigo Problem1?

Question

A bridges that crosses a river is 1km long. From 1 point on the river, the angle of elevation of the top of the bridge is 62.6 degrees. From a point 20m closer to the bridge, the angle of elevation of the top of the bridge is 72.8 degrees. How high is the bridge above the water, to the nearest meter?

Answer 1

Let the distance from bridge to second point be x and the height of the bridge be y

so tan(62.6) = y/(20+x) => y = 1.929(20+x)
and tan(72.8) = y/x => y = 3.23x
Solving the above eqautions we get the value of y as 95.84 m
so the heigh of the bridge above water is 96 m

Answer 2

1km is irrelevant.
Let h be height of bridge.
Let x be distance of foot of bridge from first point.
x - 20 is then distance of foot of bridge from 2nd point.
tan 62.6 = h/x
tan 72.8 = h / (x - 20)
x.tan 62.6° = (x - 20).tan 72.8°
x.(tan72.8° - tan 62.6°) = 20.tan 72.8°
x = 20.tan 72.8° / 1.3
x = 49.7 m
tan 62.6° = h / 49.7
h = 95.9 m