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
[tex]\dfrac{a}{\sin A}= \dfrac{b}{\sin B}= \dfrac{c}{\sin C}[/tex]
So here In Δ YSE,
[tex]\dfrac{YE}{\sin S}= \dfrac{SE}{\sin Y}= \dfrac{YS}{\sin E}[/tex]
substituting the given values we get
[tex]\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\°[/tex]
Therefore
m∠Y = 41.1°
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
[tex]\dfrac{a}{Sina}[/tex] = [tex]\dfrac{b}{Sinb}[/tex] = [tex]\dfrac{c}{Sinc}[/tex]
So, from figure
[tex]\dfrac{EY}{Sin S}[/tex] = [tex]\dfrac{SE}{Sin Y}[/tex]
Compare with sin Law
[tex]\dfrac{a}{Sina}[/tex] = [tex]\dfrac{b}{Sinb}[/tex]
Or, [tex]\frac{10}{Sin 70^{\circ}}[/tex] = [tex]\frac{7}{Sin x^{\circ}}[/tex]
Or, [tex]\dfrac{10}{0.9396}[/tex] = [tex]\frac{7}{Sin x^{\circ}}[/tex]
Or, 10.642 = [tex]\frac{7}{Sin x^{\circ}}[/tex]
Or, Sin x° = [tex]\dfrac{7}{10.642}[/tex]
Or, Sin x° = 0.65777
∴ x = [tex]Sin^{-1}0.65777[/tex]
i.e x = 41.1°
So,The measure of angle Y = x = 41.1°
Hence, The measure of angle Y is 41.1° Answer
