# trig

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The high level bridge, a railway bridge that crosses the Oldman River is over 1km long. From one 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 brige above the river, to the nearest meter? i don't understand how to do this question.. please help!!:(

• trig -

let h be height. Let d be the distance from the first observation to the bridge.

h/d=tan62.6
and
h/(d-20)=tan72.8

in the first equation

d=h ctn62.6
second equation
d=h ctn72.8 +20tan72.8
set these two equations equal, and solve for h.

• trig -

or....

Consider the triangle formed with 20 m as the base and the two lines forming the angles of elevation to the top of the bridge.
62.6 will be the interior angle and 72.8 would be an exterior angle at the 20 m base.
That would make the interior angle at the base 107.2 and the small angle at the top where the lines meet at the bridge equal to 10.2 degrees.

by the Sine Law we can find the length of the line formed by the 72.8 degree line of observation.
this then becomes the hypotenuse of a right angled triangle where h is the height of the bridge, the side found above is the hypotenuse and the base angle is 72.8.
A simple sine ratio will find the height.

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