Answer:
The length of the side opposite the smallest angle of the triangle is 2 centimeter.
Step-by-step explanation:
Given : The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters.
To find: The length of the side opposite the smallest angle of the triangle is?
Solution :
Let x be the angle of the triangle.
The angles of a triangle are in the ratio 11 : 5 : 2.
Sum of angles of the triangle is 180°.
So, [tex]11x + 5x + 2x = 180[/tex]
[tex]18x = 180[/tex]
[tex]x=10[/tex]
Therefore, The angles of the triangles are 110, 50,20 degrees.
Now, Applying Law of Sines:
i.e, to find the remaining sides of a triangle when two angles and a side are known we apply,
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}[/tex]
Let A=110°(as largest angle), a=5.5 cm(given)
B=20° (as 20 is the smallest angle), b=b(smallest length)
Substitute,
[tex]\frac{\sin 110}{5.5}=\frac{\sin 20}{b}[/tex]
Cross multiply,
[tex]b=\frac{\sin 20\times 5.5}{\sin 110}[/tex]
[tex]b=2.00[/tex]
Therefore, The length of the side opposite the smallest angle of the triangle is 2 centimeter.
