Question

solve this trigonometric equation​

Answer 1

AD = 8 cm

BC = 12 cm

As, AD is the median to BC.

$\bold{\therefore BD=DC= \frac{BD}{2} = \frac{12}{2} =6 cm}$

In ΔABD

$\bold{AB^2=AD^2+BD^2=(8)^2+(6)^2}$

$\bold{ \implies \: AB = \sqrt{64 + 36} = 10 \: cm}$

Similarly,

AC = 10 cm.

Now,

$\bold{ \tan \: x = \frac{AD}{BD} = \frac{8}{6} = \frac{4}{3} }$

$\bold{ \tan y \: = \frac{CD}{AD} = \: \frac{6}{8} = \frac{3}{4} }$

$\bold{ \therefore \: x \times \tan \: y \: = \frac{4}{3} \times \frac{3}{4} }$

=1