Question

in a triangle ABC right angled at B , AC = 20cm and tan angle ABC = 3/4 . calculate the measures of AB and BC.

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Answer 1

Answer:

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Answer 2

Answer:

Tan ACB= 3/4

Tan ACB= opposite side/adjacent side = 3/4 = AB/BC

AB = 3 parts BC = 4 parts

By Pythagoras theorem:

AB² + BC² = AC²

Since 3/4 is a ratio:

3² + 4² = AC²

25 = AC²

AC = √25 = 5 parts [consider only positive root]

Given, AC = 20 cm

AC= 5 parts = 20 cm

1 part = 20/5 = 4 cm

AB = 3 parts = 3x4 = 12 cm

BC = 4 parts = 4x4 = 16 cm