Trigonometry

Step 1: Understanding the Concept:
This is a trigonometry problem involving angles of elevation. Complementary angles are two angles that add up to 90 degrees. We can use the tangent function to relate the height of the tower to the distances and angles.
Step 2: Key Formula or Approach:
Let 'h' be the height of the tower.
Let the two points be at distances 'a' and 'b' from the base (a=5m, b=20m).
Let the angles of elevation be and . A standard result for this setup is that the height of the tower .
Step 3: Detailed Explanation:
Let the height of the tower be h. The two points are at distances 5 m and 20 m from the base.
Let the angle of elevation from the point at 20 m be .
So, -- (1)
The angle of elevation from the point at 5 m is complementary, so it is .
So, -- (2)
Using the trigonometric identity , we can rewrite equation (2):

Since , we can multiply the two tangent expressions:

We know that .


m (Height must be positive).
Step 4: Final Answer:
The height of the tower is 10 m.

Let the ladder length = 10 m, angle with ground = 45°.
We need to find the distance of foot of ladder from the wall, i.e., the base BC in right triangle ABC.
Using trigonometric relation for the base: