Question

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

Answer 1

Answer:

The measure of angle Y is 41.1°

Step-by-step 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

$\dfrac{a}{Sina}$ = $\dfrac{b}{Sinb}$ = $\dfrac{c}{Sinc}$

So, from figure

$\dfrac{EY}{Sin S}$ = $\dfrac{SE}{Sin Y}$

Compare with sin Law

$\dfrac{a}{Sina}$ = $\dfrac{b}{Sinb}$

Or, $\frac{10}{Sin 70^{\circ}}$ =  $\frac{7}{Sin x^{\circ}}$

Or, $\dfrac{10}{0.9396}$ =   $\frac{7}{Sin x^{\circ}}$

Or, 10.642 =   $\frac{7}{Sin x^{\circ}}$

Or, Sin x° = $\dfrac{7}{10.642}$

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

Answer:

Therefore

m∠Y = 41.1°

Step-by-step 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

$\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}$

So here In Δ YSE,

$\dfrac{YE}{\sin S}= \dfrac{SE}{\sin Y}= \dfrac{YS}{\sin E}$

substituting the given values we get

$\dfrac{10}{\sin 70}= \dfrac{7}{\sin Y}\\\\\sin Y=\dfrac{0.939\times 7}{10}=0.6577\\\\Y=\sin^{-1}0.6577=41.1\°$

Therefore

m∠Y = 41.1°