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The answer is 57.3 provided by my teacher, I need help with the work

The answer is 57.3 provided by my teacher, I need help with the work-example-1
User Turtaru
by
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1 Answer

4 votes

Apply the angles sum property in the triangle ABC,


62+90+\angle ACB=180\Rightarrow\angle ACB=180-152=28^{}

Similarly, apply the angles sum property in triangle BCD,


20+90+\angle BCD=180\Rightarrow\angle BCD=180-110=70

From triangle ABC,


BC=AC\sin 62=30\sin 62\approx26.5

From triangle BDC,


BD=BC\cos 20=26.5\cos 20\approx24.9

Now, consider that,


\angle BDE+\angle BDC=180\Rightarrow\angle BDE+90=180\Rightarrow\angle BDE=90

So the triangle BDE is also a right triangle, and the trigonometric ratios are applicable.

Solve for 'x' as,


x=\tan ^(-1)((BD)/(DE))=\tan ^(-1)((24.9)/(16))=57.2764\approx57.3

Thus, the value of the angle 'x' is 57.3 degrees approximately.ang

User Mamoo
by
6.6k points
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