Question

You are driving into st. louis, missouri, and in the distance you see the famous gateway-to-the-west arch. this monument rises to a height of 192 m. you estimate your line of sight with the top of the arch to be 9.53 ° above the horizontal. approximately how far (in kilometers) are you from the base of the arch?

Answer 1

Height of the monument is given by

`H = 192 m`

angle = 9.53 degree

now by geometry

`tan\theta = (H)/(d)`

`tan9.53 = (192)/(d)`

`d = 1143.67 m`

so its distance is 1143.67 m