Question

In a right angled triangle, the hypotenuse is $2\sqrt{2}$ times the perpendicular drawn from the opposite vertex.Then the other acute angles of the triangle are

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{8}$
• C. $\frac{3\pi }{8}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (B), (C)

$\frac{3\pi }{8}$
$\frac{\pi }{8}$

$p^2{\sec }^2\theta +p^{2}cose{c}^2\theta ={\left(2\sqrt{2}\right)}^2{p}^2$
$\Rightarrow \frac{1}{{\sin }^2{\cos }^2\theta }=8$
$\Rightarrow {\sin }^{2}2\theta =1/2={\left(1/\sqrt{2}\right)}^2$
$\Rightarrow 2\theta =\left(n\pi \right)\pm \left(\pi /4\right),n\in Z$
$\Rightarrow \theta =\left(n\pi /2\right)\pm \left(\pi /8\right)$
$\Rightarrow$ for $n=0,\theta =\pi /8$
$\Rightarrow$ for $n=1,\theta =3\pi /8$