A ladder manufacturing company manufactures a foldabel step ladder as shown below :
The lengths of legs AB and AC are 120 cm each.
(i) If vertical ∠BAC = 36°, what is the ratio of ∠BAC and ∠ACB ?
(ii) (a) If vertical ∠BAC = 60°, what is the length of BC?
(b) Which type of triangle is △ABC ?

Question

A ladder manufacturing company manufactures a foldabel step ladder as shown below :
The lengths of legs AB and AC are 120 cm each.
(i) If vertical ∠BAC = 36°, what is the ratio of ∠BAC and ∠ACB ?
(ii) (a) If vertical ∠BAC = 60°, what is the length of BC?
(b) Which type of triangle is △ABC ?

KnowledgeBoat · Accepted Answer

Given, AB = AC = 120 cm So, it is an isosceles triangle. ∴ ∠ABC = ∠ACB (Angles opposite to equal sides are equal in a triangle) Let ∠ABC = x (i) Sum of angles in a triangle is 180 . ∠BAC + ∠ABC + ∠ACB = 180 36 + x + x = 180 2x = 180 - 36 2x = 144 x = x = 72 So, ∠ABC = ∠ACB = 72 ∠BAC : ∠ACB = 36 : 72 = 1 : 2. Hence, ratio = 1 : 2. (ii) (a) ∠BAC = 60 Since AB = AC, So, ∠ABC = ∠ACB Sum of angles = 180 ∠BAC + ∠ABC + ∠ACB = 180 60 + 2(∠ACB) = 180 2(∠ACB) = 180 - 60 2(∠ACB) = 120 ∠ACB = ∠ACB = 60 . ∴ ∠ACB = ∠ABC = 60 Since all the three angles are 60 , so all the three sides must be equal. ∴ BC = AB = AC = 120 cm. Hence, BC = 120 cm. (b) Since all angles are 60 and all sides are equal (= 120 cm) ∴ △ ABC is an equilateral triangle. Hence, △ABC is an equilateral triangle.

Mathematics

Triangles

Related Questions

In quadrilateral ABCD, side AB is the longest and side DC is the shortest. Prove that :
(i) ∠C > ∠A
(ii) ∠D > ∠B

In triangle ABC, side AC is greater than side AB. If the internal bisector of angle A meets the opposite side at point D, prove that : ∠ADC is greater than ∠ADB.

In isosceles triangle ABC, sides AB and AC are equal. If point D lies in base BC and point E lies on BC produced (BC being produced through vertex C), prove that :
(i) AC > AD
(ii) AE > AC
(iii) AE > AD

Given : ED = EC
Prove : AB + AD > BC.

Mathematics

A ladder manufacturing company manufactures a foldabel step ladder as shown below :The lengths of legs AB and AC are 120 cm each.(i) If vertical ∠BAC = 36°, what is the ratio of ∠BAC and ∠ACB ?(ii) (a) If vertical ∠BAC = 60°, what is the length of BC?(b) Which type of triangle is △ABC ?

Triangles

Related Questions

In quadrilateral ABCD, side AB is the longest and side DC is the shortest. Prove that :(i) ∠C > ∠A(ii) ∠D > ∠B

In triangle ABC, side AC is greater than side AB. If the internal bisector of angle A meets the opposite side at point D, prove that : ∠ADC is greater than ∠ADB.

In isosceles triangle ABC, sides AB and AC are equal. If point D lies in base BC and point E lies on BC produced (BC being produced through vertex C), prove that :(i) AC > AD(ii) AE > AC(iii) AE > AD

Given : ED = ECProve : AB + AD > BC.

In quadrilateral ABCD, side AB is the longest and side DC is the shortest. Prove that :
(i) ∠C > ∠A
(ii) ∠D > ∠B

In isosceles triangle ABC, sides AB and AC are equal. If point D lies in base BC and point E lies on BC produced (BC being produced through vertex C), prove that :
(i) AC > AD
(ii) AE > AC
(iii) AE > AD

Given : ED = EC
Prove : AB + AD > BC.