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Question

The angles of elevation of the top of a tower at two points, which are at distances a and b from the foot in the same horizontal line and on the same side of the tower, are complementary. The height of the tower is


A

ab

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B

ab

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C

ab

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D

ba

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Solution

The correct option is B

ab


Step 1: Consider the following figure that represents the problem

Suppose AB is the tower and C and D are the points of observations on AC.

Step 2: Determine the height from point A

From the figure, it is clear that,

tanθ=hah=atanθ1

Step 3: Determine the height from point B

tan90-θ=hbh=btan90-θ2

Step 4: Compute the height of the tower

Multiply, the equation 1 and 2,

h2=abtanθ·cotθh=ab

Hence, option B is the correct answer.


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