Question

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

Answer 1

The angle F = 47.25°

Explanation:

Step(i):-

Given that f =42inches and e = 39 inches

Given that ∠E = 43°

By using sine rule

`(a)/(sinA) = (b)/(sinB) = (C)/(sinC) = 2R`

`(e)/(sinE) = (f)/(sinF)`

⇒
`(39)/(sin43) = (42)/(sinF)`

Cross multiplication , we get

⇒ 39 sin F = 42 × sin 43°

`sin F = (42 X 0.68199)/(39)`

⇒ sin F = 0.734459

Step(ii):-

⇒ sin⁻¹ (sin F)= sin ⁻¹ ( 0.734459)

⇒ F = 47.25

The angle F = 47.25°