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 7.82 ° above the horizontal. approximately how far (in kilometers) are you from the base of the arch?

You know from SOH CAH TOA that the tangent gives the ratio of the opposite side of a right triangle (height of the arch) to the adjacent side (distance to the arch). That is ...

... Tan(θ) = O/A

... tan(7.82°) = (0.192 km)/(distance to arch)

Multiplying by the denominator and dividing by the tangent gives ...

... distance to arch = 0.192 km/tan(7.82°) ≈ 1.398 km

You are 1.398 km from the arch.

x is variable or an unknown value to find

example:

2x = 5 which means x = 3