Question

with reference to the figure, sin x =

Answer 1

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 $\sin 63.43 =0.89438856$.

Answer 2

Trigonometry deals with the sides and angles of the triangle.

The value of sin x is 0.8943.

What is trigonometry?

It deals with the sides and angles of the triangle. Triangle is a polygon that has three sides and three angles. And the sum of all internal angles is 180.

Given

DC = 16 BC = 17.89

To find

The value of sin x?

In right-angle triangle BDC.

$\begin{aligned} \rm cos\ y &=\rm \dfrac{base}{hypotenuse} \\\\\rm cos\ y &= \dfrac{16}{17.89}\\\\ \rm y &= 26.57^{o} \end{aligned}$

In ΔABC angle B is 90.

The sum of all internal angles is 180°, then

$\begin{aligned} \rm x + y + 90^{o} &= 180^{o} \\\rm x + 26.57^{o} + 90^{o} &= 180^{o}\\\rm x &= 180^{o} - 26.57^{o} - 90^{o} \\\rm x &= 63.43^{o} \\\end{aligned}$

Then the value of sin x is 0.8943.

More about the Trigonometry link is given below.

https://brainly.com/question/6904750