Using the measurements given in the following figure :
(i) Find the value of sin Φ and tan θ.
(ii) Write an expression for AD in terms of θ.

Question

Using the measurements given in the following figure : (i) Find the value of sin Φ and tan θ. (ii) Write an expression for AD in terms of θ.

KnowledgeBoat · Accepted Answer

(i) In Δ BCD, ⇒ BD2 = BC2 \+ CD2 (∵ BD is hypotenuse) ⇒ 132 = 122 \+ CD2 ⇒ 169 = 144 \+ CD2 ⇒ CD2 = 169 \- 144 ⇒ CD2 = 25 ⇒ CD = ⇒ CD = 5 sin Φ = Draw a line parallel to BC from point D such that it meets AB at point E. This line DE will be ⊥ to AB. From figure, DE = BC = 12 In Δ BED, ⇒ BD2 = BE2 \+ DE2 (∵ BD is hypotenuse) ⇒ 132 = BE2 \+ 122 ⇒ 169 = BE2 \+ 144 ⇒ BE2 = 169 \- 144 ⇒ BE2 = 25 ⇒ BE = ⇒ BE = 5 And, AE = AB \- BE = 14 \- 5 = 9 tan θ = Hence, sin Φ = and tan θ = (ii) sin θ = sin θ = AD = = 12 cosec θ cos θ = cos θ = AD = = 9 sec θ Hence, AD = 12 cosec θ or 9 sec θ.

Mathematics

Using the measurements given in the following figure :
(i) Find the value of sin Φ and tan θ.
(ii) Write an expression for AD in terms of θ.

Trigonometric Identities

Related Questions

In the figure, given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find :
(i) sin B
(ii) tan C.
(iii) sin² B + cos² B
(iv) tan C - cot B

If sin A + cosec A = 2; find the value of sin² A + cosec² A.

Mathematics

Using the measurements given in the following figure :(i) Find the value of sin Φ and tan θ.(ii) Write an expression for AD in terms of θ.

Trigonometric Identities

Related Questions

In the figure, given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find :(i) sin B(ii) tan C.(iii) sin2 B + cos2 B(iv) tan C - cot B

If sin A + cosec A = 2; find the value of sin2 A + cosec2 A.

Using the measurements given in the following figure :
(i) Find the value of sin Φ and tan θ.
(ii) Write an expression for AD in terms of θ.

In the figure, given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find :
(i) sin B
(ii) tan C.
(iii) sin² B + cos² B
(iv) tan C - cot B

If sin A + cosec A = 2; find the value of sin² A + cosec² A.