For ΔDEF, Where e=52, f=41 and ∠F=48°. Find all the possible ∠E to the nearest degree.
The possible ∠E to the nearest degree is ∠E=70°
Given that,
ΔDEF with e=52 and f=41 sides of the triangle.
Angle ∠F=48°.
We have to find ∠E=?
By using the Law of sine
The relationship between the sides and angles of non-right (oblique) triangles is known as the Law of Sines. It simply states that for all sides and angles of a given triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same.
If triangle ABC are there with sides a, b, and c then Law of sine is
[tex]\frac{a}{SinA} =\frac{b}{SinB} =\frac{c}{SinC}[/tex]
Now, in the given triangle we have e and f sides so we take
[tex]\frac{SinE}{e}=\frac{SinF}{f}\\[/tex]
Substituting the values of e, f and F
We get,
[tex]\frac{SinE}{52}=\frac{Sin48^\circ}{41}\\ SinE=\frac{Sin48^\circ}{41}\times52\\SinE=\frac{52}{41} \times Sin48^\circ\\SinE=1.268\times 0.743\\SinE=0.942\\E=Sin^{-1}(0.942)\\[/tex]
∠E=70°
Therefore, The possible ∠E to the nearest degree ∠E=70°.
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