Using the measurements given in the figure alongside,
(a) Find the values of:
(i) sin Φ
(ii) tan θ.
(b) Write an expression for AD in terms of θ.

Question

Using the measurements given in the figure alongside, (a) Find the values of: (i) sin Φ (ii) tan θ. (b) Write an expression for AD in terms of θ.

KnowledgeBoat · Accepted Answer

(a) In right-angled ∆BCD Using pythagoras theorem we get : ⇒ BD² = BC² + CD² ⇒ CD² = BD² - BC² ⇒ CD² = (13)² - (12)² ⇒ CD² = 169 - 144 ⇒ CD² = 25 ⇒ CD = = 5. (i) By formula, sin Φ = In right-angled ∆BCD sin Φ = . Hence, sin Φ = . (ii) Draw DE perpendicular to AB. From figure, ED = BC = 12 In right-angled ∆BED Using pythagoras theorem we get : ⇒ BD² = ED² + EB² ⇒ 13² = 12² + EB² ⇒ EB² = (13)² - (12)² ⇒ EB² = 169 - 144 ⇒ EB² = 25 ⇒ EB = = 5. From figure, AE = AB - EB = 14 - 5 = 9. By formula, tan θ = . Hence, tan θ = . (b) In right-angled ∆AED Hence, AD = .

Mathematics

Using the measurements given in the figure alongside,
(a) Find the values of:
(i) sin Φ
(ii) tan θ.
(b) Write an expression for AD in terms of θ.

Trigonometrical Ratios

Related Questions

In the figure (2) given below, ∆ABC is right-angled at B and BD is perpendicular to AC. Find :
(i) cos ∠CBD
(ii) cot ∠ABD

Prove the following:
(sin A + cos A)² + (sin A - cos A)² = 2

Mathematics

Using the measurements given in the figure alongside,(a) Find the values of:(i) sin Φ(ii) tan θ.(b) Write an expression for AD in terms of θ.

Trigonometrical Ratios

Related Questions

In the figure (2) given below, ∆ABC is right-angled at B and BD is perpendicular to AC. Find :(i) cos ∠CBD(ii) cot ∠ABD

Prove the following:(sin A + cos A)2 + (sin A - cos A)2 = 2

Using the measurements given in the figure alongside,
(a) Find the values of:
(i) sin Φ
(ii) tan θ.
(b) Write an expression for AD in terms of θ.

In the figure (2) given below, ∆ABC is right-angled at B and BD is perpendicular to AC. Find :
(i) cos ∠CBD
(ii) cot ∠ABD

Prove the following:
(sin A + cos A)² + (sin A - cos A)² = 2