Question

In the given figure tan∅=​

Answer 1

$\dag \: \underline{\sf AnsWer :}$

Here we are given a right angle traingle with measure of three sides and given one angle ⊖. and we are asked to find the value of tan ⊖.

• AB = 12 units
• AC = 13 units
• BC = 5 units

First we will find the value of sin ⊖ :

$:\implies\sf \sin( \theta) = \dfrac{Opposite \: side}{Hypotenuse}$

$:\implies\sf \sin( \theta) = \dfrac{AB}{AC}$

$:\implies \underline{ \boxed{\sf \sin( \theta) = \dfrac{12}{13}}}$

Also find the value of cos ⊖ :

$\dashrightarrow\:\:\sf \cos( \theta) = \dfrac{Adjacent \: side}{Hypotenuse}$

$\dashrightarrow\:\:\sf \cos( \theta) = \dfrac{BC}{AC}$

$\dashrightarrow\:\: \underline{ \boxed{\sf \cos( \theta) = \dfrac{5}{13} }}$

Now, we can find the value of tan ⊖ :

$\longrightarrow\:\:\sf \tan(\theta) = \dfrac{\sin (\theta)}{\cos(\theta)}$

$\longrightarrow\:\:\sf \tan(\theta) = \dfrac{ \dfrac{12}{13}}{ \dfrac{5}{13}}$

$\longrightarrow\:\:\sf \tan(\theta) = \dfrac{12}{13} \times \dfrac{13}{5}$

$\longrightarrow\:\:\sf \tan(\theta) = \dfrac{12}{13} \times \dfrac{13}{5}$

$\longrightarrow\:\: \underline{ \boxed{\sf \tan(\theta) = \dfrac{12}{5}}}$

Answer 2

12/5 is the right answer