Question

How do you find the missing length of an Isosceles triangle given base = 8 and angle = 30?

Answer 1

Hint:
Divide the triangle into two right angled triangles, and use its proportional properties to find the missing length.

Complete step by step solution:
First, we have to divide the triangle into two halves which form two right angled triangle, like the given below diagram, then we use its Pythagoras proportional properties, Then with the help of these proportion we equate them which leads us to the missing length of the isosceles triangles. Also, we divide the Isosceles triangle, we also divide the base into two equal halves , also the angle opposite to the base.
Since, we know that the sides of a right angled triangle are in the ratio of $2:1:\sqrt 3 $. In which the $\sqrt 3 $ proportion corresponds to the base of the triangle. And here it is the half of the base of the isosceles triangle. And the 2 other ratios correspond to the missing length.

Since we have three angles and length proportions, we can get the length of the isosceles triangle
We can make an equation for solving the missing length.
So using this we will get the length.

$\dfrac{{required\,length}}{2} = \dfrac{{Baselength}}{{\sqrt 3 }}$

Since the base has been divided into two halves, the base length is 4.
So then we get
$
  required\,length = \dfrac{{2 \times 4}}{{\sqrt 3 }} \\
  required\,length = \dfrac{8}{{\sqrt 3 }} \\
$

Note:
The sine law can be used on any triangles other than right angled triangles. The proportions of the right-angled triangle used based on the Pythagoras triangle property. Also isosceles triangle forms two right angled triangles when divided other than that no other can. It also forms an scalene triangle and right angled triangle cannot be isosceles triangles