Question

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

Answer 1

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