Answer:
From the figure,
The length of BC = 17.89 unit and the length of DC =16 unit.
Now, find the angle y by using cosine function;
Cosine defines as the ratio of the adjacent side of a right triangle to the hypotenuse
i.e \(\cos = \frac{Adjacent side}{Hpotenuse}\)
from the triangle BDC;
Hypotenuse = BC =17.89 unit and Adjacent side = 16 units
then;
\(\cos y =\frac{16}{17.89} =0.894354388\) or
\(y =\cos^{-1} (0.894354388)\) = \(26.57^{\circ}\) (nearest to hundredths place)
Now, find the value of angle x;
In right angle ΔABC;
The sum of measures of the three angles in triangle ABC is 180 degrees.
\(\angle A + \angle B +\angle C =180^{\circ}\) ....[1]
from the given figure, \(\angle B=90^{\circ}\), \(\angle A =x^{\circ}\) and
\(\angle C =y=26.57^{\circ}\)
Substitute these in [1] to solve for angle x;
\(x^{\circ}+90^{\circ}+y^{\circ} =180^{\circ}\) or
\(x^{\circ}+90^{\circ}+26.57^{\circ} =180^{\circ}\)
or
\(x^{\circ}+116.57^{\circ} =180^{\circ}\)
Simplify:
\(x^{\circ}=180^{\circ}-116.57^{\circ}=63.43^{\circ}\)
We have to find the value of sin x;
then;
The value of \(\sin 63.43 =0.89438856\).
