Answer:
The measurement of angle A is 51°
Step-by-step explanation:
Given: A triangle with some measurements.
We have to find the measurement of angle A
Consider the given triangle,
Using Sine rule,
For a , b and c be the sides of the triangle and Side a faces angle A,
side b faces angle B and side c faces angle C.
we have,
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
Here, given a = 7 in
b = 9 in
∠B = 95°
Substitute, we have,
[tex]\frac{7}{\sin A}=\frac{9}{\sin 95^{\circ}}=\frac{c}{\sin C}[/tex]
Consider the first two ratios, we have,
[tex]\frac{7}{\sin A}=\frac{9}{\sin 95^{\circ}}[/tex]
Now, Cross multiply , we have,
[tex]\sin A=\frac{7 \times \sin 95^{\circ}}{9}[/tex]
Simplify, we have,
[tex]\sin A=0.7748[/tex]
A = 51°
Thus, The measurement of angle A is 51°
