You are driving into St. Louis, Missouri, and in the distance you see the famous

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 9.9 degree above the horizontal. Approximately how far (in kilometers) are you from the base of the arch? km The two hot air balloons in the drawing are 48.2 and h = 63.0 m above the ground. A person in the left balloon observes that the right balloon is theta = 10.4 degree above the horizontal. What is the horizontal distance x between the two balloons? m

Explanation / Answer

given , volume V = 2.5 litres = 2.5*10^-3 m^3 (squinch)
volume of serroboam, v = 8.1 us gallons
now 1 us gallon = 3.78541 litres
so in 1 serroboam, 8.1*3.78541 litres = 8.1*3.78541/2.5 squinches
so in 1 serroboam there are 12.264 squnches

height of monument, h = 192 m
angle of line of siognt, theta = 7.2 degree above h orizontal
let the distance from the base of the monument be d
then tan(theta) = h/d
d = h/yan(theta) = 192/tan(7.2) = 1519.836 m
d = 1.519 km

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