SOLUTION: Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45� angle to see a hot air balloon. Emily looks up at a 60� angle to see the same hot air balloon. Appro

Question 1034851: Caleb and Emily are standing 100 yards from each other. Caleb looks up at a 45� angle to see a hot air balloon. Emily looks up at a 60� angle to see the same hot air balloon. Approximately how far is the hot air balloon off the ground?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
You'll have to draw the diagram as it is not something I can do here...
Anyway, you'l have two triangles, a 45-45-90 and a 30-60-90...we can use the law of sines to find the hypotenuse of the 30-60-90 triangle by first showing how the outside triangle has angles of 45, 120, and 15 degrees.
Call the hypotenuse of the inside triangle, c, so that
(sin 15)/100 = (sin 45)/c
which leads to
c = 100 sin 45 / sin 15 = 273.2
The height of the balloon is sqrt(3)/2 times that...or 236.6 yards...
RELATED QUESTIONS
From a hot air balloon 3 km high a person looks east and sees one town with angle of... (answered by Alan3354)

You are standing 45 feet away from a tree. To see the top of the tree you must look up at (answered by mananth)

One observer at point A estimates the angle of elevation to the basket of a hot air... (answered by TimothyLamb)

A hot-air balloon has risen to an altitude of 280m. You can still see the starting point... (answered by Mathtut)

Two observers on the ground are 2000m apart. Observer A measures the angle of elevation... (answered by rothauserc)

Math gr 10 geometry sine law? Sara is riding a hot air balloon directly over John who is (answered by scott8148)

if you are 1500 feet from a very tall tower and look up at a 45 degree angle to see the... (answered by Fombitz,Edwin McCravy)

A hot air balloon is seen over Seven Springs simultaneously by two observers standing at... (answered by josmiceli)

A man is flying in a hot-air balloon in a straight line at a constant rate of 4 feet per... (answered by josgarithmetic)