# In δ Fan, ∠ F = 80° , ∠ a = 40° . Find Out the Greatest and the Smallest Side of the Triangle. State the Reason. - Geometry

Sum

In Δ FAN, ∠ F = 80° , ∠ A = 40° . Find out the greatest and the smallest side of the triangle. State the reason.

#### Solution

In ∆FAN,
∠F + ∠A + ∠N = 180   (Angle sum property)
⇒ 80 + 40 + ∠N = 180
⇒ 120 + ∠N = 180
⇒ ∠N = 180 − 120
= 60
Now, in △FAN,  ∠F and ∠A are the largest and smallest angle.
The side opposite to the largest angle is the greatest side and the side opposite to the smallest angle is the smallest side .
Hence, the greatest and the smallest side of the triangle are AN and ​FN respectively.

Concept: Properties of inequalities of sides and angles of a triangle
Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 3 Triangles
Practice Set 3.4 | Q 4 | Page 43
The text passage contains a geometry problem that involves finding the greatest and smallest sides of a triangle given the measures of its angles. The solution is provided, explaining the steps to determine the sides based on the angles.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# In δ Fan, ∠ F = 80° , ∠ a = 40° . Find Out the Greatest and the Smallest Side of the Triangle. State the Reason. - Geometry

Sum

In Δ FAN, ∠ F = 80° , ∠ A = 40° . Find out the greatest and the smallest side of the triangle. State the reason.

#### Solution

In ∆FAN,
∠F + ∠A + ∠N = 180   (Angle sum property)
⇒ 80 + 40 + ∠N = 180
⇒ 120 + ∠N = 180
⇒ ∠N = 180 − 120
= 60
Now, in △FAN,  ∠F and ∠A are the largest and smallest angle.
The side opposite to the largest angle is the greatest side and the side opposite to the smallest angle is the smallest side .
Hence, the greatest and the smallest side of the triangle are AN and ​FN respectively.

Concept: Properties of inequalities of sides and angles of a triangle
Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 3 Triangles
Practice Set 3.4 | Q 4 | Page 43
user
The text passage contains a geometry problem that involves finding the greatest and smallest sides of a triangle given the measures of its angles. The solution is provided, explaining the steps to determine the sides based on the angles.

TYPE: SINGLE_QUESTION_WITH_ANSWER