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Question
In a right-angled triangle ABC, ∠B = 90°, BD = 3, DC = 4, and AC = 13. A point D is inside the triangle such as ∠BDC = 90°.
Find the values of 2 tan ∠BAC - sin ∠BCD
Solution
ΔBDC is a right-angled triangle.
∴ BC2
= BD2 +DC2
= 32 + 42
= 9 + 16
= 25
⇒ BC = 5cm
ΔABC is a right-angled triangle.
∴ AB2
= AC2 - BC2
= 132 - 52
= 169 - 25
= 144
⇒ AB = 12cm
2 tan ∠BAC - sin ∠BCD
= `2 xx "BC"/"AB" - "BD"/"BC"`
= `2 xx (5)/(12) - (3)/(5)`
= `(5)/(6) - (3)/(5)`
= `(25 - 18)/(30)`
= `(7)/(30)`.
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