Question

HELPPPPPPPP In WXY, y=690 cm, w=440 cm and angle X=163°. Find angle W to the nearest degree

Answer 1

Answer:

The angle W is approximately 7°.

Step-by-step explanation:

Since angle X is adjacent to sides y and w and opposite to side x, we calculate the length of side x by Law of the Cosine:

$x = \sqrt{y^2+w^2-2\cdot y\cdot w \cdot \cos X}$ (1)

Where:

$y, z$ - Side lengths, in centimeters.

$W$ - Angle, in sexagesimal degrees.

If we know that $y = 690\,cm$, $w = 440\,cm$ and $X = 163^{\circ}$, then the length of the side x is:

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

$x\approx 1118.199\,cm$

By Geometry we know that sum of internal angles in a triangle equals 180°. If X is an obtuse, then Y and W are both acute angles. By Law of the Sine we find angle W:

$\frac{x}{\sin X}= \frac{w}{\sin W}$ (2)

$\sin W = \left(\frac{w}{x} \right)\cdot \sin X$

$W = \sin^{-1}\left[\left(\frac{w}{x} \right)\cdot \sin X\right]$

If we know that $X = 163^{\circ}$, $w = 440\,cm$ and $x\approx 1118.199\,cm$, then the angle W is:

$W = \sin^{-1}\left[\left(\frac{w}{x} \right)\cdot \sin X\right]$

$W \approx 6.606^{\circ}$

Hence, the angle W is approximately 7°.