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In ΔEFG, f = 42 inches, e = 39 inches and ∠E=43°. Find all possible values of ∠F, to the nearest degree.\

Sagot :

Answer:

The angle F = 47.25°

Step-by-step explanation:

Step(i):-

Given that f =42inches  and  e = 39 inches

Given that ∠E = 43°

By using sine rule

                 [tex]\frac{a}{sinA} = \frac{b}{sinB} = \frac{C}{sinC} = 2R[/tex]

                [tex]\frac{e}{sinE} = \frac{f}{sinF}[/tex]

 ⇒          [tex]\frac{39}{sin43} = \frac{42}{sinF}[/tex]

  Cross multiplication , we get

⇒       39 sin F = 42 × sin 43°

             [tex]sin F = \frac{42 X 0.68199}{39}[/tex]

⇒           sin F = 0.734459

Step(ii):-

⇒       sin⁻¹ (sin F)= sin ⁻¹ ( 0.734459)

⇒            F = 47.25

The angle F = 47.25°

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