Trig
posted by Nikki .
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 oppisite side of the runway are 6 degrees and 13 degreess respectivel. The points and the tower are in the same vertical plane and the distance from A to B is 1.1km. Determine the height of the tower. Please give me a diagram and step by step instructions. This question has me stumped!!!

Let the base of the tower be C, and the top of the tower be T. So, the height h=CT, and we have
AB=1, so AC=x and BC=1x
h/x = tan6°
h/(1x) = tan13°
so, solve for x:
xtan6° = (1x)tan13°
x = 0.687
h = 0.0722km = 72.2m 
Can you show me the steps you used to isolate x?

x is the distance from A to the base of the tower.
Since AB=1, the distance to B is 1x.
Did you not understand the diagram points? 
oops. Sorry. I see that AB=1.1
So, adjust the equations and solve again. 
Yes I understand the diagram points and can see how you came up with this now but am having trouble coming up with an answer for
xtan6°=(1.1x)tan13°
I know this is basic but I am having trouble isolating the x!
I am getting
x=tan13°tan6°/1.1 which is giving me a negative answer. 
plugging in the trig values, you have
.1051x = .2309(1.1x)
Have you forgotten your algebra I?
.1051x = .2540  .2309x
.3360x = .2540
x = 0.756 
Lol! Apparently I have been working on this question too long! Thanks!
Respond to this Question
Similar Questions

Math
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, and , respectively. The points and the tower are in the same vertical … 
math
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 … 
math
I'm not sure how to work this problem out. Find it very confusing and my answer keeps changing. Please help. From an observation tower that overlooks a runway, the angles of depression of point A, on one side of the runway, and point … 
Math
From an observation tower that overlooks a runway, the angles of depressin of point A, on one side of the runway, and point B, on the opposite side of the runway are, 6degree and 13degree, respectively. The points and the tower are … 
Trigonometry
From an observation tower that overlooks a small lake, the angles of depression of point A, on one side of the lake, and point B, on the opposite side of the lake are, 7degrees and 13degrees, respectively. The points and the tower … 
Math
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 … 
Math/Trig
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 … 
math
An aeroplane leaves a runway and climbs at an angle of 15 degrees. After flying 800 meters, how high is it above the runway? 
Algebra
A pilot flying at an attitude of 25,000 ft. The angle of depression from her position to the start of the runway is 2 degrees. How far is the airplane from start of the runway ( in ground distance)? 
Maths
You wonder what altitude the plane reached when it was directly above the end of the runway and how far it travelled to get to that point. You know the runway tarmac is 5500 metres long and approximate that when the plane left the …