Question

What is the range of possible values for x? The diagram is not to scale.?

Answer 1

Range : 0° < x < 17°

Explanation:

In any triangle, the smallest angle is opposite to the smallest side.

So, In ΔABD, the side which faces ∠ABD is AD whose length is 22 units.....(1)

And, in ΔCBD, the side which faces ∠CBD is CD whose length is 30 units....(2)

Now, from equations (1) and (2) We get,

∠ABD < ∠CBD

So, ∠ABD lies between 0° to 34°

∴ Range of x is 0° to 17°

Answer 2

Range : 0° < x < 17°

Explanation:

In any triangle, the smallest angle is opposite to the smallest side.

So, In ΔABD , the side which faces ∠ABD is AD whose length is 22 units.....(1)

And, in ΔCBD, the side which faces ∠CBD is CD whose length is 30 units....(2)

Now, from equations (1) and (2) We get,

∠ABD < ∠CBD

So, ∠ABD lies between 0° to 34°

`\Rightarrow 0 < 2\cdot x<34\\\Rightarrow 0<x<(34)/(2)\\\Rightarrow0<x<17`

∴ Range of x is 0° to 17°