Question

With reference to the figure, sin x =

Answer 1

Cos y = 16 / 17.89 = 0.8944
y = cos^-1 (0.8944) = 26.57°

tan 26.57 = BA / 17.89
BA = 17.89 tan 26.57 = 8.95

tan x = 17.89 / 8.95 = 1.999
x = arctan 1.999 = 63.43

sin x = sin 63.43 = 0.8944

Answer 2

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 $\sin 63.43 =0.89438856$.