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प्रश्न
In right-angled triangle ABC; ∠B = 90°. Find the magnitude of angle A, if:
a. AB is `sqrt(3)` times of BC.
B. BC is `sqrt(3)` times of BC.
उत्तर
Consider the following figure,
a. Given, AB = `sqrt(3) xx "BC"`
⇒ `"AB"/"BC" = sqrt(3)`
⇒ cot θ = `sqrt(3)`
⇒ cot θ = cot30°
⇒ θ = 30°.
b. Given, BC = `sqrt(3) xx "AB"`
⇒ `"BC"/"AB" = sqrt(3)`
⇒ tan θ = `sqrt(3)`
⇒ tan θ = tan60°
⇒ θ = 60°.
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