Straight LineHardBloom L3
Question
In an isosceles right angled triangle, a straight line drawn from the mid-point of one of equal sides to the opposite angle. It divides the angle into two parts, $\theta$ and $(\pi/4 - \theta)$. Then $tan\theta$ and $tan\lbrack(\pi/4) - \theta\rbrack$ are equal to :
Options
A.$\frac{1}{2},\frac{1}{3}$
B.$\frac{1}{3},\frac{1}{4}$
C.$\frac{1}{5},\frac{1}{6}$
D.None of these
Solution
Sol. [Key Concept: Isosceles right triangle: the median to a leg splits the angle; get $\tan\ \theta$ and $\tan(\frac{\pi}{4} - \theta)$ from the geometry.]
$${tan\theta = \frac{a}{2a} = \frac{1}{2} }{tan\left( \frac{\pi}{4} - \theta \right) = \frac{1 - 1/2}{1 + 1/2} = \frac{1}{3}}$$
Create a free account to view solution
View Solution FreeMore Straight Line Questions
The straight line, $ax + by = 1$ makes with the curve $px^{2} + 2axy + qy^{2} = r$ a chord which subtends a right angle ...The line passing through the point of intersection of lines x + y − 2 = 0 and 2x − y + 1 = 0 and origin is -...The angle between the lines represented by x2 + xy = 0 is -...Consider the family of lines x(a + b) + y = 1, where a, b and c are the roots of the equation x3 - 3x2 + x + λ = 0 ...What is the $y$-intercept of the line that is parallel to $y = 3x$, and which bisects the area of a rectangle with corne...