Question

in the given fig if AB 14cm, BD 10cm and DC 8cm then the value of tan beta is

Answer 1

Step-by-step explanation:

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AB=14cm;BD=10cm;DC=8cm

DC=EA=8cm [since opposite sides are equal in a rectangle]

Then BE=AB-EA

=14-8

=6cm

given,BD=10cm

By Pythagoras theorem => BD²=ED²+BE²

=>ED²=BD²-BE²

=10²-6²

=100-36=64

ED=8cm

Now ; Tan B= opposite side / adjacent side

=ED/BE

=8/6

=4/3

Hope you understood

Answer 2

Given : AB= 14cm BD=10cm and DC=8 cm

To Find : the value of tan B ​​

Solution:

AB = AE + BE  ( segment addition postulate)

AE = DC   opposite Equal sides of rectangle

=> AB =DC + BE

=> 14 = 8 + BE

=> BE = 6 cm

    BD = 10 cm

BD²  = BE² +  DE²

=> 10² = 6² + DE²

=> DE² = 8²

=> DE = 8  

Tan B  =  DE/BE

=> tan B = 8/6

=> tan B = 4/3

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