Advertisements
Advertisements
Question
In ΔABC, if ∠A = 40° and ∠B = 60°. Determine the longest and shortest sides of the triangle.
Advertisements
Solution
Given that in , ΔABC ∠A =40° and ∠B=60° We have to find longest and shortest side We know that,
Sum of angles in a triangle180°
⇒∠A+∠B+∠C=180°
⇒40°+60°+∠C=180°
⇒∠C=180° -(40° +60° )
=180° -100° =80°
∴∠C = 80°
Now,
⇒ 40<60<80⇒∠A< ∠B < ∠C
⇒ ∠Cis greater angle and ∠A is smaller angle
Now, ∠A<∠B<∠C
⇒ BC<AAC<AB
[∵Side opposite to greater angle is larger and side opposite to smaller angle is smaller]
∴ AB is longest and BC is smallest or shortest side.
APPEARS IN
RELATED QUESTIONS
ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that
- ΔABE ≅ ΔACF
- AB = AC, i.e., ABC is an isosceles triangle.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
ABC is a triangle in which BE and CF are, respectively, the perpendiculars to the sides AC and AB. If BE = CF, prove that ΔABC is isosceles
Fill the blank in the following so that the following statement is true.
Angle opposite to equal sides of a triangle are .....
Fill the blank in the following so that the following statement is true.
In an equilateral triangle all angles are .....
Which of the following statements are true (T) and which are false (F)?
Sum of any two sides of a triangle is greater than the third side.
Which of the following statements are true (T) and which are false (F)?
Of all the line segments that can be drawn from a point to a line not containing it, the perpendicular line segment is the shortest one.
Fill in the blank to make the following statement true.
In a right triangle the hypotenuse is the .... side.
Fill in the blank to make the following statement true.
If two sides of a triangle are unequal, then the larger side has .... angle opposite to it.
If the angles of a triangle are in the ratio 2 : 1 : 3, then find the measure of smallest angle.
In a ΔABC, if ∠A = 60°, ∠B = 80° and the bisectors of ∠B and ∠C meet at O, then ∠BOC =
In the given figure, if EC || AB, ∠ECD = 70° and ∠BDO = 20°, then ∠OBD is
In the given figure, what is z in terms of x and y?
The side BC of ΔABC is produced to a point D. The bisector of ∠A meets side BC in L. If ∠ABC = 30° and ∠ACD = 115°, then ∠ALC = ______.
The angles of a right angled triangle are
In ∆ABC, AB = AC and ∠B = 50°. Then ∠C is equal to ______.
It is given that ∆ABC ≅ ∆FDE and AB = 5 cm, ∠B = 40° and ∠A = 80°. Then which of the following is true?
Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.
Find all the angles of an equilateral triangle.
