Prove your conjecture by using the identity for the tangent of the sum of two angles.
Answer to Problem 5PS
We have verified the conjecture.
Explanation of Solution
Given information:
Three squares of side length
Calculation:
Let us consider that the three adjacent squares have been kept as below.
The relation between the sum
Applying Lami’s Theorem to triangle
We obtain a relation between angle
Similarly we apply Lami’s Theorem to triangle
We obtain a relation between angle
By equation (1) and (2), we can say that
Since all the angles involved are acute, hence the above expression will hold if and only if
Considering the triangle
By equation (3) and the above expression,
The above conjecture can be proved by using sum formula for tangent for the right hand side of the equation (4) given as follows:
Similarly the tangent of the left hand side of the equation (4) can be written as follows:
Since the angles on both the sides of the equation (4) are acute and since the tangent of
Hence, we have verified the conjecture.
Chapter 5 Solutions
EBK PRECALCULUS W/LIMITS
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