Question

With reference to the figure, sin x =

Answer 1

Answer:

0.894

Step-by-step explanation:

Data provided in the question

BC length = 17.89 unit

DC length = 16 unit.

Now, we have to compute the angle y with the help of the cosine function;

Cosine defines the ratio between the right angle adjacent side and the hypotenuse  

$\cos = \frac{Adjacent side}{Hpotenuse}$

As per the triangle BDC;

Hypotenuse = BC =17.89 unit

And, the Adjacent side = 16 units

So;

$\cos y =\frac{16}{17.89} =0.894354388$

$y =\cos^{-1} (0.894354388) = 26.57^{\circ} (nearest\ to\ hundredths\ place)$

Now, determine the value of angle x

In right angle ΔABC;

As we know that

The three angles sum is 180 degrees

So,

$\angle A + \angle B +\angle C =180^{\circ} ....(1)$

According to the given figure

$\angle B=90^{\circ}, \angle A =x^{\circ}$

and

$\angle C =y=26.57^{\circ}$

Now Substitute these in (1) for solving the angle x;

$x^{\circ}+90^{\circ}+y^{\circ} =180^{\circ}$

or

$x^{\circ}+90^{\circ}+26.57^{\circ} =180^{\circ}$

or

$x^{\circ}+116.57^{\circ} =180^{\circ}$

$x^{\circ}=180^{\circ} - 116.57^{\circ}=63.43^{\circ}$

Finally we have to determine the value of sin x;

Hence,

The value of $\sin 63.43 =0.89438856$

or

= 0.894