Question

In the right angled triangle ABC, angle B=90 degree and tan C = 1/2. If AC = 6 cm, then the length of the side AB is

Answer 1

$\textbf{Given:}$

$\text{In \triangle ABC, \angle{B}=90^{\circ} , AC=6 cm and tanC=\dfrac{1}{2} }$

$\textbf{To find:}$

$\text{Length of AB}$

$tanC=\dfrac{1}{2}$

$\implies\dfrac{AB}{BC}=\dfrac{1}{2}=k\text{(say)}$

$\implies\,AB=k\;\text{and}\;BC=2k$

$\text{By pythagoras theorem,}$

$AB^2+BC^2=AC^2$

$k^2+4k^2=36$

$5k^2=36$

$k^2=\dfrac{36}{5}$

$\implies\bf\,k=\dfrac{6}{\sqrt{5}}$

$\therefore\textbf{The length of AB= is \dfrac{6}{\sqrt{5}} cm}$

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Answer 2

Answer:

6/√5

Step-by-step explanation:

Let's make a rough diagram.

We have, tan Z = 1/2 = P/B

Thus, ratio of perpendicular to base is 1/2 so we can assume perpendicular = x and base = 2x

By Pythagoras theorem

6 ^ 2 = x ^ 2 + (2x) ^ 2

Rightarrow 36 = x ^ 2 + 4x ^ 2

Rightarrow x ^ 2 = 50/5

Rightarrow x = 6/(sqrt(5))

AB = x = v/(sqrt(6)) cm and BC = 2x = 12/(sqrt(6)) cm