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3 years ago

6

What is the range of possible values for x?

1 answer:

Talja [164]3 years ago

7 0

The minimum value for 2x is 0
<span>the maximum value is achieved when A, D and C are collinear and the quadrilateral ABCD becomes an isosceles triangle ABC </span>
<span>base AB = 52 and vertical angle 2x + 34° </span>

<span>For the sine law </span>
<span>(sin 2x)/22 = (sin ADB)/AB </span>
<span>(sin 34°)/30 = (sin BDC)/BC </span>

<span>is given that AB = BC, and sin ADC = sin BDC because they are supplementary, so from </span>
<span>(sin ADC)/AB = (sin BDC)/BC </span>

<span>it follows </span>
<span>(sin 2x)/22 = (sin 34°)/30 </span>

<span>sin 2x = 22 (sin 34°)/30 </span>

<span>2x = asin(22 (sin 34°)/30) ≈ 24.2° </span>

<span>x = 0.5 asin(22 (sin 34°)/30) ≈ 12.1° </span>

<span>0 < x < 12.1°</span>

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