Trigonometry in square

Geometry Level 3

Find the value of tan[φ] if O is on the square's line of symmetry.

90-θ 2-tanθ tan(90-θ) Cannot be determined

Archit Boobna by Archit Boobna , 20, India

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2 solutions

Varun Agarwal
Sep 11, 2014

2-tanθ is the right answer

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can you explain

nikhil jaiswal - 6 years, 8 months ago

please show the solution

Bikash Jena - 6 years, 6 months ago

Please explain

Ratnangshu Das - 6 years, 6 months ago

Please explain

Omkar Kulkarni - 6 years, 4 months ago

Also, there is more than one line of symmetry.

Marta Reece - 4 years, 1 month ago
Tom Engelsman
Oct 7, 2016

Let the square have side length of x. Also, let tan(theta) = |OO'| / (x/2) and tan(phi) = (x - |OO'|) / (x/2), where O' is the midpoint of the square's bottom-most side. Solving for tan(phi) gives:

tan(phi) = (x - |OO'|) / (x/2) = [x - (x/2) tan(theta)] / (x/2) = [1 - (1/2) tan(theta)] / (1/2) = 2 [1 - (1/2) tan(theta)] = 2 - tan(theta).

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