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kodGreya [7K]
3 years ago
8

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

Mathematics
1 answer:
zavuch27 [327]3 years ago
7 0

Answer:

The angle F = 47.25°

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that f =42inches  and  e = 39 inches

Given that ∠E = 43°

By using sine rule

                 \frac{a}{sinA} = \frac{b}{sinB} = \frac{C}{sinC}  = 2R

                \frac{e}{sinE} = \frac{f}{sinF}

 ⇒          \frac{39}{sin43} = \frac{42}{sinF}

  Cross multiplication , we get

⇒       39 sin F = 42 × sin 43°

             sin F = \frac{42 X 0.68199}{39}

⇒           sin F = 0.734459

<u><em>Step(ii):-</em></u>

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

⇒            F = 47.25

The angle F = 47.25°

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