SOLUTION: Find Height of Arch <IMG SRC="http://image.prntscr.com/image/10c002eb6658420394424c9f7cf1c161.jpg" ALT="some text" WIDTH=700 HEIGHT=500>

Algebra ->  Triangles -> SOLUTION: Find Height of Arch <IMG SRC="http://image.prntscr.com/image/10c002eb6658420394424c9f7cf1c161.jpg" ALT="some text" WIDTH=700 HEIGHT=500>      Log On


   

Question 1036186: Find Height of Arch some text
Found 2 solutions by richard1234, robertb:
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
where x is the distance from the 80-degree angle endpoint to the midpoint of the base of the arch.



Then . Substitute expression for x into the first equation to obtain:



Solve for h, and use your calculator to evaluate and .

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the distance of the foot of the axis of the arch from the vertex of angle 80%5Eo.
Then tan80%5Eo+=+h%2Fx, and tan69%5Eo+=+h%2F%28x%2B131%29.
The first equation gives x+=+h%2Ftan80%5Eo.
Substituting this into the 2nd equation gives
tan69%5Eo+=+h%2F%28h%2Ftan80%5Eo+%2B131%29.
==> tan69%5Eo+=+%28htan80%5Eo%29%2F%28h%2B131tan80%5Eo%29
==> htan69%5Eo+%2B+131%2Atan80%5Eo%2Atan69%5Eo+=+htan80%5Eo
==> h+=+%28131%2Atan80%5Eo%2Atan69%5Eo%29%2F%28tan80%5Eo+-+tan69%5Eo%29+=+631.2 feet, the height of the Gateway Arch.