In figure if AB= 14cm BD=10cm and DC=8 cm then the value of tan B
Answers
Step-by-step explanation:
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
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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