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प्रश्न
In triangle ABC; ∠ABC = 90°, ∠CAB = x°, tan x° = `(3)/(4)` and BC = 15 cm. Find the measures of AB and AC.
उत्तर
Consider the figure:
tan x° = `(3)/(4)`
i.e. `"perpendicular"/"base" = "BC"/"AB" =(3)/(4)`
Therefore if length of base = 4x, length of perpendicular = 3x
Since
BC2 + AB2 = AC2 ...[Using Pythagoras Theorem]
(3x)2 + (4x)2 = AC2
AC2 = 9x2 + 16x2
AC2 = 25x2
AC = `sqrt(25x^2)`
∴ AC = 5x
Now
BC = 15
3x = 15
x = `15/3`
x = 5
Therefore
AB = 4x
= 4 × 5
= 20 cm
And
AC = 5x
= 5 × 5
= 25 cm
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