In /_\DEF,e=840 inches, d=760 inches and /_D=134^(@). Find all possible values of /_E, to the nearest degree. Answer:

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In  /_\DEF,e=840 inches,  d=760 inches and  /_D=134^(@). Find all possible values of  /_E, to the nearest degree. Answer:

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Apply Law of Sines: To find the possible values of /_E, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all three sides of the 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 opposite angles. In this case, we have side e and angle D, so we can set up the ratio for side e and angle E.Find Sine of Angle D: First, we need to find the sine of angle D. Since /_D is 134 degrees, we can calculate: $$ \sin(D) = \sin(134^\circ) $$ Using a calculator, we find that: $$ \sin(134^\circ) \approx 0.656059 $$Set Up Ratio for Side e: Now, we can set up the Law of Sines ratio for side e and angle E: $$ \frac{e}{\sin(E)} = \frac{d}{\sin(D)} $$ Substituting the known values, we get: $$ \frac{840}{\sin(E)} = \frac{760}{0.656059} $$Solve for Sin(E): Solving for sin(E), we have: $$ \sin(E) = \frac{840}{\frac{760}{0.656059}} $$ $$ \sin(E) = \frac{840 \times 0.656059}{760} $$ $$ \sin(E) \approx \frac{551.08956}{760} $$ $$ \sin(E) \approx 0.725118 $$Calculate Angle E: To find angle E, we take the inverse sine (arcsin) of 0.725118: $$ E = \arcsin(0.725118) $$ Using a calculator, we find that: $$ E \approx 46.57^\circ $$ Since we need to round to the nearest degree, /_E is approximately 47 degrees.However, we must consider that there could be another possible value for angle E because the sine function is positive in both the first and second quadrants. Since the sum of angles in a triangle must be 180 degrees, we can find the other possible value for angle E by subtracting angle D and our found angle E from 180 degrees: $$ 180^\circ - 134^\circ - 47^\circ = -1^\circ $$ This result is not possible because angles in a triangle cannot be negative. Therefore, there is only one possible value for angle E.

In $\triangle \mathrm{DEF}, e=840$ inches, $d=760$ inches and $\angle \mathrm{D}=134^{\circ}$ . Find all possible values of $\angle \mathrm{E}$ , to the nearest degree. $\newline$ Answer:

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In △DEF,e=840 \triangle \mathrm{DEF}, e=840 △DEF,e=840 inches, d=760 d=760 d=760 inches and ∠D=134∘ \angle \mathrm{D}=134^{\circ} ∠D=134∘. Find all possible values of ∠E \angle \mathrm{E} ∠E, to the nearest degree.\newlineAnswer:

In $\triangle \mathrm{DEF}, e=840$ inches, $d=760$ inches and $\angle \mathrm{D}=134^{\circ}$ . Find all possible values of $\angle \mathrm{E}$ , to the nearest degree. $\newline$ Answer: