Question

Can anyone help me with this qeustion I need it for math today.

Answer 1

The measure of angle Y is 41.1°

Explanation:

Given as :

The figure is of triangle YES

The measure of angle S = ∠a = 70°

Let The measure of angle Y = ∠b = x°

The measure of side EY = a = 10 unit

The measure of side SE = b = 7 unit

Now, According o question

From The Law of Sin

`(a)/(Sina)` =
`(b)/(Sinb)` =
`(c)/(Sinc)`

So, from figure

`(EY)/(Sin S)` =
`(SE)/(Sin Y)`

Compare with sin Law

`(a)/(Sina)` =
`(b)/(Sinb)`

Or,
`(10)/(Sin 70^(\circ))` =
`(7)/(Sin x^(\circ))`

Or,
`(10)/(0.9396)` =
`(7)/(Sin x^(\circ))`

Or, 10.642 =
`(7)/(Sin x^(\circ))`

Or, Sin x° =
`(7)/(10.642)`

Or, Sin x° = 0.65777

∴ x =
`Sin^(-1)0.65777`

i.e x = 41.1°

So,The measure of angle Y = x = 41.1°

Hence, The measure of angle Y is 41.1° Answer

Answer 2

Therefore

m∠Y = 41.1°

Explanation:

Given:

In Δ YSE ,

m∠S = 70°

YE = 10 = side opposite to ∠Y

SE = 7 = side opposite to ∠S

To Find:

m∠Y = ?

Solution:

In Δ ABC, Sine Rule says

`(a)/(\sin A)= (b)/(\sin B)= (c)/(\sin C)`

So here In Δ YSE,

`(YE)/(\sin S)= (SE)/(\sin Y)= (YS)/(\sin E)`

substituting the given values we get

`(10)/(\sin 70)= (7)/(\sin Y)\\\\\sin Y=(0.939* 7)/(10)=0.6577\\\\Y=\sin^(-1)0.6577=41.1\°`

Therefore

m∠Y = 41.1°