Posted by jasmine on Sunday, July 21, 2013 at 10:26pm.
From an observation tower that overlooks a runway, the angles of depression of point A, on one side of the runway, and point B, on the opposite side of the runway are, 6 degrees and 13 degrees, respectively. The points and the tower are in the same vertical plane and the distance from A to B is 1.1 km. Determine the height of the tower.
Can someone help me solve this? I am confused on how this is laid out, can someone draw some kind of picture, i have no idea where to put the angles and tower/road.

Math  Reiny, Sunday, July 21, 2013 at 11:09pm
Assume we are taking a side view,
draw a straight line, label the left end A and the right end B
Place a point between them to represent the tower, and give it some height.
Join both A and B to the top of the tower
You now have 2 rightangled triangles.
where the base angle at A is 6° and at B is 13°
let the distance from A to the base of the tower be x
then the distance from B to the base of the tower is 1.1  x
let the height of the tower be h
in the triangle containing A
tan 6° = h/x > h = xtan6
in the triangle containing B
tan 13° = h/(1.1x) > h = (1.1  x)tan13
xtan6 = 1.1tan13  xtan13
x(tan6 + tan13) = 1.1tan13
x = 1.1tan13/(tan6 + tan13) = .3441195
h = xtan6 = .03616..
all units are in km, so the tower is .036 km or appr 36 m high

Math  jasmine, Monday, July 22, 2013 at 11:49pm
thank you, makes more sense, i thought it was supposed to look like that but its just worded poorly, and the vertical plane got me confused.
Answer This Question
Related Questions
 math  From an observation tower that overlooks a runway, the angles of ...
 math  I'm not sure how to work this problem out. Find it very confusing and my ...
 Math  From an observation tower that overlooks a runway, the angles of ...
 Math  From an observation tower that overlooks a runway, the angles of ...
 Trig  From an observation tower that overlooks a runway, the angles of ...
 Math/Trig  From an observation tower that overlooks a runway, the angles of ...
 Trigonometry  From an observation tower that overlooks a small lake, the angles...
 Maths  You wonder what altitude the plane reached when it was directly above ...
 Algebra  A pilot flying at an attitude of 25,000 ft. The angle of depression ...
 math  An aeroplane leaves a runway and climbs at an angle of 15 degrees. After ...
More Related Questions