Question

In ∆XYZ, m∠X = 152, y = 15, and z = 19. Find side x and the measure of angle Y to the nearest tenth

Answer 1

The measure of the side $x$ is approximately 33 and the measure of angle $Y$ is approximately 12.321°.

How to find a missing angle in a triangle by law of sine and law of cosine

In this problem we must apply the law of cosine and the law of sine to determine the angle Y:

Law of cosine

$x = \sqrt{y^{2}+z^{2}-2\cdot y\cdot z\cdot \cos X}$

$x = \sqrt{15^{2}+19^{2}-2\cdot (15)\cdot (19)\cdot \cos 152^{\circ}}$

$x \approx 33$

Law of sine

$\frac{\sin Y}{y} = \frac{\sin X}{x}$

$Y = \sin^{-1}\left(\frac{y}{x}\cdot \sin X \right)$

$Y = \sin^{-1}\left(\frac{15}{33}\cdot \sin 152^{\circ} \right)$

$Y \approx 12.321^{\circ}$

The measure of the side $x$ is approximately 33 and the measure of angle $Y$ is approximately 12.321°. $\blacksquare$

To learn more on triangles, we kindly invite to check this verified question: brainly.com/question/25813512