In /_\WXY,x=450 inches, w=220 inches and /_W=157^(@). Find all possible values of /_X, to the nearest 1oth of a degree. Answer:

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In  /_\WXY,x=450 inches,  w=220 inches and  /_W=157^(@). Find all possible values of  /_X, to the nearest 1oth of a degree. Answer:

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Apply Law of Sines: To find the possible values of angle X, we can use the Law of Sines, which relates the sides of a triangle to its angles. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle. The formula is: $$ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} $$ where $ a, b, $ and $ c $ are the lengths of the sides, and $ A, B, $ and $ C $ are the measures of the opposite angles.Find Angle Y: First, we need to find the measure of angle Y using the fact that the sum of angles in a triangle is 180 degrees. We have: $$ \angle W + \angle X + \angle Y = 180^\circ $$ Given that $ \angle W = 157^\circ $, we can write: $$ 157^\circ + \angle X + \angle Y = 180^\circ $$Express Angle X: To find $ \angle Y $, we need to express $ \angle X $ in terms of $ \angle Y $ or vice versa. Since we don't have any information about $ \angle X $ yet, we can express it as: $$ \angle X = 180^\circ - 157^\circ - \angle Y $$ $$ \angle X = 23^\circ - \angle Y $$Use Law of Sines: Now we can use the Law of Sines to relate the sides and angles. We have: $$ \frac{x}{\sin(\angle X)} = \frac{w}{\sin(\angle W)} $$ Substituting the given values, we get: $$ \frac{450}{\sin(\angle X)} = \frac{220}{\sin(157^\circ)} $$Calculate Sin X: We can now solve for $ \sin(\angle X) $ by cross-multiplying and then use the inverse sine function to find $ \angle X $. However, we must be careful because the inverse sine function can give us an angle less than 90 degrees, but since $ \angle X $ is supplementary to $ \angle Y $, we need to consider that $ \angle X $ could be obtuse (greater than 90 degrees). Let's first calculate $ \sin(\angle X) $: $$ \sin(\angle X) = \frac{450 \cdot \sin(157^\circ)}{220} $$Using a calculator to find $ \sin(157^\circ) $ and then calculating $ \sin(\angle X) $: $$ \sin(157^\circ) \approx 0.999048 $$ $$ \sin(\angle X) \approx \frac{450 \cdot 0.999048}{220} $$ $$ \sin(\angle X) \approx 2.041 $$ This value is greater than 1, which is not possible for a sine value. This indicates that there has been a math error in the calculation.

In $\triangle \mathrm{WXY}, x=450$ inches, $w=220$ inches and $\angle \mathrm{W}=157^{\circ}$ . Find all possible values of $\angle \mathrm{X}$ , to the nearest $10$ th of a degree. $\newline$ Answer:

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In △WXY,x=450 \triangle \mathrm{WXY}, x=450 △WXY,x=450 inches, w=220 w=220 w=220 inches and ∠W=157∘ \angle \mathrm{W}=157^{\circ} ∠W=157∘. Find all possible values of ∠X \angle \mathrm{X} ∠X, to the nearest 101010th of a degree.\newlineAnswer:

In $\triangle \mathrm{WXY}, x=450$ inches, $w=220$ inches and $\angle \mathrm{W}=157^{\circ}$ . Find all possible values of $\angle \mathrm{X}$ , to the nearest $10$ th of a degree. $\newline$ Answer: