Answer
402.9k+ views
Hint: Problems of this type have non-specific answers, this means that we will be able to find the range between which the answer lies. Using a trigonometric formula of isosceles triangle, we will get the limits between which the length of the third side of an isosceles triangle can exist. So, we can take any value between the limits and conclude it as the answer to the problem.
Complete step by step answer:
For an isosceles triangle if the given two sides have the same length then for calculating the length of the third side of the triangle, we can use a trigonometric formula for finding the length of the unknown side of the triangle, which is
$l=2\cdot a\cdot sin\left( \dfrac{\theta }{2} \right)$
Here, $l$ is the length of the third side of the triangle, $a$ is the length of the other two sides of the triangle and $\theta $ is the angle between the similar sides of the triangle.
The angle $\theta $ lies between $0$ to $\pi $
We know that $\sin \left( \dfrac{0}{2} \right)=0$ and $\sin \left( \dfrac{\pi }{2} \right)=1$
From the formula we get
$l=2\cdot 15\cdot sin\left( \dfrac{0}{2} \right)$
$\Rightarrow l=0$ , when $\theta =0$
Also, $l=2\cdot 15\cdot sin\left( \dfrac{\pi }{2} \right)$
$\Rightarrow l=30$ , when $\theta =\pi $
As the angle $\theta $ can take any value between the range $\left( 0,\pi \right)$ the length of the third side of an isosceles triangle can take any value between the range $\left( 0,30 \right)$ .
Therefore, we can conclude that the third side of an isosceles triangle can be of any length between $0$ and $30$ .
Note:
The problem can also be solved by applying the property of triangles. According to a property of triangles the sum of any two sides is greater than the third and the difference between any two sides is less than the third. So, in this case the lower limit for the length of the third side is $0$ and the upper limit for the length of the third side is $30$ . As, $15-15=0$ and $15+15=30$ .
Complete step by step answer:
![seo images](https://www.vedantu.com/question-sets/90060b8c-e1e5-456c-b5f9-196e1be3bf716902476536760510586.png)
For an isosceles triangle if the given two sides have the same length then for calculating the length of the third side of the triangle, we can use a trigonometric formula for finding the length of the unknown side of the triangle, which is
$l=2\cdot a\cdot sin\left( \dfrac{\theta }{2} \right)$
Here, $l$ is the length of the third side of the triangle, $a$ is the length of the other two sides of the triangle and $\theta $ is the angle between the similar sides of the triangle.
The angle $\theta $ lies between $0$ to $\pi $
We know that $\sin \left( \dfrac{0}{2} \right)=0$ and $\sin \left( \dfrac{\pi }{2} \right)=1$
From the formula we get
$l=2\cdot 15\cdot sin\left( \dfrac{0}{2} \right)$
$\Rightarrow l=0$ , when $\theta =0$
Also, $l=2\cdot 15\cdot sin\left( \dfrac{\pi }{2} \right)$
$\Rightarrow l=30$ , when $\theta =\pi $
As the angle $\theta $ can take any value between the range $\left( 0,\pi \right)$ the length of the third side of an isosceles triangle can take any value between the range $\left( 0,30 \right)$ .
Therefore, we can conclude that the third side of an isosceles triangle can be of any length between $0$ and $30$ .
Note:
The problem can also be solved by applying the property of triangles. According to a property of triangles the sum of any two sides is greater than the third and the difference between any two sides is less than the third. So, in this case the lower limit for the length of the third side is $0$ and the upper limit for the length of the third side is $30$ . As, $15-15=0$ and $15+15=30$ .
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)