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XAT 2019 — QA & DI Question 11

Basics of QuadrilateralsEasy

In the trapezium ABCD the sides AB and CD are parallel. The value of sin∠BACsin∠BAD is

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Answer & solution

  • AD/AC

  • B

    AB/CD

  • C

    BC/AD

  • D

    AC/AD

  • E

    AC/CD

Solution

Refer the diagram below:

In ∆ACL,
Sin∠BAC = Sin∠LAC = perpendicular/hypotenuse = CL/AC   …(1)

Similarly, in ∆ADM,
Sin∠BAD = Sin∠MAD = DM/AD   …(2)

(1) ÷ (2)

⇒ Sin∠BAC : Sin∠BAD = CL/AC : DM/AD

Now, CL = DM

Hence, Sin∠BAC : Sin∠BAD = 1/AC : 1/AD = AD : AC

Hence, option (a).

XAT 2019 QA & DI Q11: In the trapezium ABCD the sides AB and CD are parallel. The value of sin ∠ B A C sin ∠ B A D is ​​ — Solution | TheCATExam