Trigonometry & Inverse Trigonometry
Right Triangle Properties
Grade 11
Question:
<p>In a right angled triangle ABC, the bisector of the right angle C divides AB into segments x and y. If \(\tan\frac{A-B}{2} = t\), then x : y is equal to</p>
<p>(a) (1+t):(1-t)</p>
<p>(b) (1-t):(1+t)</p>
<p>(c) 1:(1+t)</p>
<p>(d) (1-t):1</p>
Step-by-Step Solution
Key Concept: Apply the angle bisector theorem combined with the tangent of half-angle difference formula.
<p>In a right-angled triangle with the right angle at C, the angle bisector from C divides the hypotenuse AB in the ratio of the adjacent sides. Using the angle bisector theorem and the given condition \(\tan\frac{A-B}{2} = t\), we can derive that \(x:y = (1+t):(1-t)\).</p>
Correct Answer: A