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Question 18
A right-angled triangle ABC is right-angled at B, and tan A = $$\dfrac{3}{4}$$. If AC = 25 cm, the length of BC is:
Solution
From Pythagoras theorem, $AC^2 = AB^2 + BC^2$
=> $BC^2 = AC^2 - AB^2$
=> $16x^2 = 625 - 9x^2$
=> $25x^2 = 625$
=> $x^2 = 25$
=> x = 5
Therefore, BC = 4x = 4*5 = 20 cm
From Pythagoras theorem, $AC^2 = AB^2 + BC^2$
=> $BC^2 = AC^2 - AB^2$
=> $16x^2 = 625 - 9x^2$
=> $25x^2 = 625$
=> $x^2 = 25$
=> x = 5
Therefore, BC = 4x = 4*5 = 20 cm
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