In the adjoining figure, cosec x = , AB = 26 cm and sin y = . Find BC.

Question

KnowledgeBoat · Accepted Answer

By formula, sin θ = cosec θ = In ΔABD, Since, ΔABD is a right angled triangle. Using pythagoras theorem, ⇒ AB2 = BD2 + AD2 ⇒ 262 = 102 + AD2 ⇒ 676 = 100 + AD2 ⇒ AD2 = 676 - 100 ⇒ AD2 = 576 ⇒ AD = ⇒ AD = 24 cm As length of side of a triangle cannot be negative. So, AD = 24 cm. In ΔADC, Since, ΔADC is a right angled triangle. Using pythagoras theorem, ⇒ AC2 = AD2 + DC2 ⇒ 512 = 242 + DC2 ⇒ 2601 = 576 + DC2 ⇒ DC2 = 2601 - 576 ⇒ DC2 = 2025 ⇒ DC = ⇒ DC = 45 As length of side of a triangle cannot be negative. So, DC = 45 cm. From figure, BC = BD + DC = 10 + 45 = 55 cm. Hence, the length of BC = 55 cm.

Mathematics

In the adjoining figure, cosec x = , AB = 26 cm and sin y = . Find BC.

Trigonometrical Ratios

Related Questions

Given 4 sin θ = 3 cos θ, find the values of :
(i) sin θ
(ii) cos θ
(iii) cot² θ - cosec² θ

Mathematics

In the adjoining figure, cosec x = , AB = 26 cm and sin y = . Find BC.

Trigonometrical Ratios

Related Questions

Given 4 sin θ = 3 cos θ, find the values of :(i) sin θ(ii) cos θ(iii) cot2 θ - cosec2 θ

Given 4 sin θ = 3 cos θ, find the values of :
(i) sin θ
(ii) cos θ
(iii) cot² θ - cosec² θ