Given:
Let A denote the angle of the given triangle which measures ∠A = 81°
Let B denote the angle which measures ∠B = 40°
The length of the side a = x.
The length of the side b = 7 cm.
We need to determine the value of x.
Value of x:
The value of x can be determined using the law of sine formula.
Applying the law of sine, we have;
[tex]\frac{sin \ A}{a}=\frac{sin \ B}{b}[/tex]
Substituting the values, we have;
[tex]\frac{sin \ 81^{\circ}}{x}=\frac{sin \ 40^{\circ}}{7}[/tex]
Simplifying, we get;
[tex]\frac{0.988}{x}=\frac{0.643}{7}[/tex]
Cross multiplying, we have;
[tex]0.988 \times 7=0.643 x[/tex]
[tex]6.916=0.643x[/tex]
[tex]10.8=x[/tex]
Thus, the length of the side x is 10.8 cm.
Following are the calculation to find the x:
Given:
Assuming the triangle is ABC:
then
[tex]\angle A=81^{\circ}\\\\\angle B=40^{\circ}\\\\a= 7\ cm\\\\[/tex]
To find:
x=?
Solution:
To find the x value we use the Law of sine:
[tex]\to \bold{\frac{\sin A}{a} =\frac{\sin B}{ b}}[/tex]
Putting the given value:
[tex]\to \frac{\sin 81^{\circ}}{x}= \frac{\sin 40^{\circ}}{7}\\\\ \to \frac{0.988}{x} =\frac{0.643}{7}\\\\\to \frac{0.988 \times 7}{0.643} =x\\\\\to x= \frac{0.988 \times 7}{0.643} \\\\\to x= \frac{6.916 }{0.643} \\\\\to x=10.755\approx 10.8[/tex]
Therefore, the final answer is "10.8 cm".
Learn more:
brainly.com/question/21444145
