Question

With reference to the figure, sin x =

Answer 1

sin x = 0.894

Explanation:

I hope you are refering to this figure:

Answer 2

0.894

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 = (Adjacent side)/(Hpotenuse)`

As per the triangle BDC;

Hypotenuse = BC =17.89 unit

And, the Adjacent side = 16 units

So;

`\cos y =(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