Question

In ΔWXY, y = 88 cm, x = 85 cm and ∠X=70°. Find all possible values of ∠Y, to the nearest 10th of a degree.

Answer 1

No Possible triangles

Explanation:

Answer 2

All possible values of ∠Y are 76.6° and 103.4°

Explanation:

In Δ WXY

∵ x is the opposite side of ∠X

∵ y is the opposite side of ∠Y

→ By using the sine rule

∴
`(x)/(sin(X))` =
`(y)/(sin(Y))`

∵ x = 85 and y = 88

∴ m∠X = 70°

→ Substitute them in the rule above

∴
`(85)/(sin(70))` =
`(88)/(sin(Y))`

→ By using the cross multiplication

∴ 85 × sin(Y) = 88 × sin(70)

→ Divide both sides by 85

∴ sin(Y) = 0.9728582427

∴ m∠Y =
`sin^(-1)`(0.9728582427)

∴ m∠Y = 76.62037845

→ Round it to the nearest tenth

∴ m∠Y = 76.6°

→ The other value of ∠Y is the obtuse angle supplement of ∠Y

∴ m∠Y = 180 - 76.6

∴ m∠Y = 103.4°

∴ All possible values of ∠Y are 76.6° and 103.4°