In ΔABC, m∠B=90, AC+BC=25 and AB=5, determine the value of sinA, cosA and tanA.
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in ABC , m∠B=90°
so, AC is hypotenuse , BC is assumed as base and AB is altitude .
Let , AC = x
then, BC = 25 - AC [ from question]
BC = 25 - x
now use Pythagoras theorem,
AC² = BC² + AB²
=> x² = (25 - x)² + 5²
=> x² = 625 + x² - 50x + 25
=> 650 - 50x = 0
=> x = 13
so, AC = 13 , BC = 25 - 13 = 12
now sinA = BC/AC = 12/13
cosA = AB/AC = 5/13
tanA = BC/AB = 12/5
so, AC is hypotenuse , BC is assumed as base and AB is altitude .
Let , AC = x
then, BC = 25 - AC [ from question]
BC = 25 - x
now use Pythagoras theorem,
AC² = BC² + AB²
=> x² = (25 - x)² + 5²
=> x² = 625 + x² - 50x + 25
=> 650 - 50x = 0
=> x = 13
so, AC = 13 , BC = 25 - 13 = 12
now sinA = BC/AC = 12/13
cosA = AB/AC = 5/13
tanA = BC/AB = 12/5
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