Geometry Help for Unit Review

Question

^{(1) A tower has an observation deck about 330 m above ground level. About how far is it from the observation deck to the horizon knowing that the Earth's radius is 6400 km?}

 

^{(2) What is the locus of points in space that are r units from a point A?}

Answer 1

(1)

 

h = height of observation deck = 330 m

 

R = radius of earth = 6,400,000 m

 

d = distance from observation deck to horizon = ?

 

You have a right triangle of hypotenuse R + h, and perpendicular sides of length d and R

 

(R + h)² = R² + d²

 

R² + 2Rh + h² = R² + d²

 

2Rh + h² = d²

 

d = √(2Rh + h²) = √[2(6,400,000)(330) + (330)²] m ≅  64,993 m = 64.993 km

 

(2)

 

That is a sphere or radius r centered at A.