In DeltaUVW,w=5.3cm,v=4.8cm and /_V=151^(@). Find all possible values of /_W, to the nearest 1oth of a degree. Answer:

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In  DeltaUVW,w=5.3cm,v=4.8cm and  /_V=151^(@). Find all possible values of  /_W, to the nearest 1oth of a degree. Answer:

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Use Law of Sines: Use the Law of Sines to find the ratio of the sides to the sines of their opposite angles. $$ \frac{w}{\sin W} = \frac{v}{\sin V} $$ Substitute the given values into the equation. $$ \frac{5.3}{\sin W} = \frac{4.8}{\sin 151^\circ} $$Calculate sine of V: Calculate the sine of angle V. $$ \sin 151^\circ \approx 0.5150 $$Substitute and solve: Substitute the value of sin V into the equation and solve for sin W. $$ \frac{5.3}{\sin W} = \frac{4.8}{0.5150} $$ $$ \sin W = \frac{5.3 \times 0.5150}{4.8} $$ $$ \sin W \approx \frac{2.7295}{4.8} $$ $$ \sin W \approx 0.5686 $$Find possible values of W: Find the possible values of angle W using the inverse sine function. $$ W \approx \sin^{-1}(0.5686) $$ Since the sine function has a range of [-1, 1] and is positive in the first and second quadrants, there are two possible angles for W: one acute and one obtuse. $$ W_1 \approx \sin^{-1}(0.5686) $$ $$ W_2 \approx 180^\circ - W_1 $$Calculate first W: Calculate the first possible value of angle W. $$ W_1 \approx \sin^{-1}(0.5686) $$ $$ W_1 \approx 34.7^\circ $$Calculate second W: Calculate the second possible value of angle W. $$ W_2 \approx 180^\circ - 34.7^\circ $$ $$ W_2 \approx 145.3^\circ $$Check triangle angles: Check if the sum of angles in the triangle exceeds 180 degrees when using the second possible value of angle W. $$ 151^\circ + 145.3^\circ > 180^\circ $$ This is not possible in a triangle, so the only valid solution for angle W is the acute angle.

In $\Delta \mathrm{UVW}, w=5.3 \mathrm{~cm}, v=4.8 \mathrm{~cm}$ and $\angle \mathrm{V}=151^{\circ}$ . Find all possible values of $\angle \mathrm{W}$ , to the nearest $10$ th of a degree. $\newline$ Answer:

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In ΔUVW,w=5.3 cm,v=4.8 cm \Delta \mathrm{UVW}, w=5.3 \mathrm{~cm}, v=4.8 \mathrm{~cm} ΔUVW,w=5.3 cm,v=4.8 cm and ∠V=151∘ \angle \mathrm{V}=151^{\circ} ∠V=151∘. Find all possible values of ∠W \angle \mathrm{W} ∠W, to the nearest 101010th of a degree.\newlineAnswer:

In $\Delta \mathrm{UVW}, w=5.3 \mathrm{~cm}, v=4.8 \mathrm{~cm}$ and $\angle \mathrm{V}=151^{\circ}$ . Find all possible values of $\angle \mathrm{W}$ , to the nearest $10$ th of a degree. $\newline$ Answer: