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Question
If ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC =7units, find ∠B, AB and AC.
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Solution
∠C = 90°, ∠A = 45°
∠A + ∠B + ∠C = 180°
45° + ∠B + 90° = 180°
∠B = 180° - 135°
∠= 45°
sin45° = `"BC"/"AB"`
⇒ AB = `"BC"/"sin45°"`
⇒ AB = `(7)/(1/sqrt(2)`
⇒ AB = `7sqrt(2)"units"`
Also,
tan45° = `"BC"/"AC"`
⇒ AC = `"BC"/tan45°"`
⇒ AC = `(7)/(1)`
⇒ AC = 7units.
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