Answer:
The measure of an angle A=[tex]1^{\circ}[/tex].
Step-by-step explanation:
We are given that an angle [tex]95^{\circ}[/tex] and two sides are 7 in and 9 in in a given figure.
We have to find the value of measurement of angle A.
To find the measurement of angle A we apply sine law.
Sine law:[tex]\frac{a}{sin \alpha}=\frac{b}{sin\beta}=\frac{c}{sin \gamma}[/tex]
Where side a is opposite to angle [tex]\alpha[/tex]
Side b is opposite to angle [tex]\beta[/tex]
Side c is opposite to angle[tex] \gamma[/tex]
We are given an angle 95 degrees and opposite side of given angle is 9 in and the angle A is opposite to side 7 in.
Substituting the values then we get
[tex]\frac{9}{sin 95^{\circ}}=\frac{7}{sin A}[/tex]
[tex]\frac{9}{0.683}=\frac{7}{sin A}[/tex]
[tex] sin A=\frac{7\times 0.683}{9}[/tex]
[tex] sin A=\frac{4.781}{9}=\frac{4781}{9000}[/tex]
[tex] sin A=0.531[/tex]
[tex] A= sin^{-1}(0.531)[/tex]
[tex] A=0.56^{\circ}[/tex]
[tex] A= 1^{\circ}[/tex]
Hence, the measure of an angle A=[tex]1^{\circ}[/tex].
