Q1 of 76 Page 11

In Δ ABC, if ∠A=40° and ∠B=60°. Determine the longest and shortest sides of the triangle.

Given that in Δ ABC

∠A = 40o and ∠B = 60o


We have to find shortest and longest side.


We know that,


Sum of angles of triangle = 180o


∠A + ∠B + ∠C = 180o


40o + 60o + ∠C = 180o


100o + ∠C = 180o


∠C = 180o – 100o


= 80o


Now,


40o < 60o < 80o


∠A < ∠B < ∠C


∠C is greater angle and ∠A is smaller angle.


As, ∠A < ∠B < ∠C


BC < AC < AB (Therefore, side opposite to greater angle is larger and side opposite to smaller angle is smaller)


Therefore, AB is longest and BC is smallest or shortest side.


More from this chapter

All 76 →
6

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.


(ii) Angles opposite to equal sides of a triangle are equal.


(iii) The measure of each angle of an equilateral triangle is 60°.


(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.


(v) The bisectors of two equal angles of a triangle are equal.


(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.


(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.


(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.


(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

 7

Fill in the blanks in the following so that each of the following statements is true.

(i) Sides opposite to equal angles of a triangle are ………


(i) Sides opposite to equal angles of a triangle are …………..


(iii) In an equilateral triangle all angles are ……….


(iv) In a Δ ABC, if ∠A=∠C, then AB = ………


(v) If altitudes CE and BF of a triangle ABC are equal, then, AB = ……..


(vi) In an isosceles triangle ABC with AB=AC, if BD and CE are its altitudes, then BD is ….CE.


(vii) In right triangles ABC and DEF, if hypotenuse AB=EF and side AC=DE, then Δ ABC ≅ Δ …….

 2

In a Δ ABC, if ∠B=∠C =45°, which is the longest side?

 3

In Δ ABC, side AB is produced to D so that BD=BC. If ∠B=60° and ∠A=70°, prove that:

(i) AD > CD (ii) AD > AC