In triangle DEF, the all possible values of ∠D is 52⁰ and 128⁰.
What is triangle?
A triangle is "closed, 2D shape with 3 sides, 3 Angles and 3 vertices".
According to the question,
In ΔDEF, d = 740 inches, f = 690 inches and ∠F = 47°
Law of sines is [tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] where a, b, c are sides of the triangle and A, B, C are angles of the triangle.
Using Law of sines and applying reciprocal we get [tex]\frac{sinA}{a}[/tex]=[tex]\frac{sinB}{b}[/tex] .
a = d = 740 inches, b = f = 690 inches, ∠A=∠D and ∠B = ∠F.
∠F = 47°.
[tex]\frac{sinD}{740}[/tex]=[tex]\frac{sin47}{690}[/tex] .
[tex]sinD = \frac{740sin47}{690}[/tex] ≈ 0.7843
[tex]D = sin^-1(0.7843)[/tex] ≈ 51.66 = 52°
Quadrant II: 180° - 52° = 128°.
To check for possibility
47° + 52° =99° [This is possible because 99° is less than 180°]
47° + 128° =175° [This is possible because 175° is less than 180°]
Hence, the triangle DEF, the all possible values of ∠D is 52⁰ and 128⁰.
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