Posted by Anonymous on Wednesday, July 15, 2009 at 12:57pm.
A building 24 m tall is viewed from the top and bottom of a vertical ladder.The building forms an angle of 45 degrees with the top of the ladder and an angle of 60 degrees with the bottom of the ladder.Find
(i) the height of the vertical ladder
(ii) the distance between the building and the ladder
- Math - MathMate, Wednesday, July 15, 2009 at 7:58pm
The top of the building forms an angle of 45 degrees with the top of the ladder...
I believe the question means the top of the building makes 45 and 60 degrees with the horizontal, and not the building itself (i.e. from bottom to top).
In this case, the distance from the building is
The height of the ladder is
24m - d.tan(45)
= 24 - 8sqrt(3)
= 10.144 m.
If the angles are subtented by the top and bottom of the building, the feasible solution of the height of the ladder is higher than the building, as if it is a ladder from a fire-truck.
In this case, we calculate the centre of a circle which passes through the top and bottom of the building, and subtends an angle of 90 deg. It is a point at 12 m from the face of the building and 12 m. high above ground. The radius of the circle is r=12sqrt(2) m.
From here we find the intersection with the ladder at d=8sqrt(3) from the building. There is one intersection above ground at a height of
h = 12m + sqrt(r2+(d-r)2)
=12 + sqrt(144*2 + (13.856-12)2)
=12 + sqrt(288+ 3.446)
= 29.07 m.
- Math - MathMate, Wednesday, July 15, 2009 at 8:07pm
A sketch is available at the following link:
Answer This Question
More Related Questions
- Math trig - a ladder 24 feet long leans against the side of a building, and the...
- geometry - a ladder is placed next to a building to get to the top. the bottom ...
- calculus - a ladder 6 feet long leans against a vertical building. the bottom of...
- Precalculus - A 28 foot ladder just reaches the top of a building and forms an ...
- algebra 2 - A ladder of 25ft is placed against a building in such a way that the...
- trigonometry - A 10 meter ladder is leaning against the side of a building. If ...
- geometry - A 24 foot ladder forms a 76 degree angle with the ground. The top of ...
- math word problems - A ladder is leaning against a building. The distance from ...
- Geometry - John is painting the side of a building that is 30ft tall. The ladder...
- Geometry/ SAT Math - This was an SAT question of the day, but I can't figure out...