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Question
In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC
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Solution
Sum of angles in Δle = 180°
∠A + ∠B + ∠C = 180°
45° + ∠B + 90° = 180°
∠B = 180° − 135°
∠B = 45°
From figure `cos B = (BC)/(AB)`
`cos 45^2 = 7/(AB)`
`1/sqrt2 . 7/(AB)`
`AB = 7sqrt2 units`
From figure `sin B = (AC)/(AB)`
`sin 45^@ = (AB)/(7sqrt2)`
`1/sqrt2 = (AC)/(7sqrt2)`
∴ AC = 7 units
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