MathematicsIn the given figure, if AB=14 cm , then the value of tanB is:

In the given figure, if $AB = 14 cm$ , then the value of $tan B$ is:

A
$43$
B
$143$
C
$53$
D
$133$

Solution:

From the figure, it is given that

D C = A E = 5

cm .
We have to find the value of

tan B .

In a right-angle triangle ABC, it is right angled at

B

. Then, tangent

A

can be written as,

tan A = side opposite to angle A side adjacent to angle A .

So,

B E = A B − A E ⇒ B E = 14 − 5 ⇒ B E = 9 c m

In a right-angle triangle DEA, it is right angled at

E

.
So, applying Pythagoras theorem,

A D 2 = A E 2 + E D 2 ⇒ 132 = 52 + E D 2 ⇒ E D 2 = 144 ⇒ E D = 12 cm

So,

tanB = \frac{ED}{BE}

\Rightarrow tanB = \frac{12}{9}

\Rightarrow tanB = \frac{4}{3}

The value of

tan b = 43

.
Therefore, the correct option is 1.