Question

Q9. In the given figure, ABC is a right triangle. D is the midpoint of BC.
Show that tan theta /tan® = 1/2
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Answer 1

Solution:

We know that

$tan \: = \frac{perpendicular}{base}$
so,in the given figure

$tan \: \theta = \frac{AC}{BC} \\ \\ tan \: \phi = \frac{AC}{DC} \\ \\ .....eq1$
Since it is given that D is tha midpoint of BC,So we can write

BC= 2DC

$tan \: \theta = \frac{AC}{2DC} \\ \\ \\ .....eq2$

Now divide both equations

$\frac{tan \: \theta }{tan \: \phi} = \frac{AC}{2DC} \times \frac{DC}{AC} \\ \\ \\ \frac{tan \: \theta }{tan \: \phi} = \frac{1}{2}$
hence proved

Answer 2

Answer:

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