Question

The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the side opposite the smallest angle of the triangle is ? centimeters

Answer 1

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, $11x + 5x + 2x = 180$

$18x = 180$

$x=10$

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,

$\frac{\sin A}{a}=\frac{\sin B}{b}$

Let A=110°(as largest angle), a=5.5 cm(given)

B=20° (as 20 is the smallest angle), b=b(smallest length)

Substitute,

$\frac{\sin 110}{5.5}=\frac{\sin 20}{b}$

Cross multiply,

$b=\frac{\sin 20\times 5.5}{\sin 110}$

$b=2.00$

Therefore, The length of the side opposite the smallest angle of the triangle is 2 centimeter.

Answer 2

The side opposite the lasrgest angle will also be the largest side in the triangle

Here it s 5.5 cms.

so using the given ratios we have

2/11 = x /5.5   where x is the smallest side (opposite the smallest angle)

x = (2*5.5) / 11  =  1 cm.