Question

While taking a ride in a hot air balloon in Napa Valley, Francisco wonders how high he is.

Answer 1

let landmark be at L 
ZN = 100, NL = x (say) 
tan 54 = (100+x)/H 
100 + x = H tan 54 -------------- (1) 
------------------------------ 
tan 61 = H/x ................ [alternate angle] 
x = H cot 61 ------------------------- (2) 
put x from (2) into (1) 
H cot 61 + 100 = H tan 54 
H = 100 / [tan 54 -cot 61] 
H = 100 / [1.376 - 0.554] 
H = 121.65 feet