Question

2. Find the value of x and y rounded to the nearest tenth.

Answer 1

Using relations in a right triangle, it is found that the values of x and y are given by: x = 24, y = 46.4, given by option a.

What are the relations in a right triangle?

The relations in a right triangle are given as follows:

• The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

• The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

• The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

First, we start with the vertical line h that divides y, that is opposite to an angle of 30º, with hypotenuse 34, hence:

sin(30º) = h/34

0.5 = h/34

h = 17.

Then, h is opposite to an angle of 45º, while the hypotenuse is x, hence:

$\sin{45^\circ} = \frac{17}{x}$

$x = \frac{17}{\sin{45^\circ}}$

x = 24.

y is divided into two segments.

• The first is the adjacent to the angle of 30º, while the hypotenuse is 34.

• The second is adjacent to the angle of 45º, while the hypotenuse is 24.

Then:

$\cos{30^\circ} = \frac{y_1}{34}$

$y_1 = 34\cos{30^\circ} = 29.4$

$\cos{45^\circ} = \frac{y_2}{24}$

$y_2 = 24\cos{45^\circ} = 17$

Then, the value of y is given by:

$y = y_1 + y_2 = 29.4 + 17 = 46.4$.

More can be learned about relations in a right triangle at brainly.com/question/26396675

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