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

In right angle ∆ABC, ⇒ AC 2 = AB 2 + BC 2 ⇒ AC 2 = 12 2 + 5 2 ⇒ AC 2 = 144 + 25 ⇒ AC 2 = 169 ⇒ AC = = 13. Let ∠CBD = x. ∠DBA = 90° - x In ∆DAB, ⇒ ∠DAB + ∠ADB + ∠DBA = 180° [Angle sum property of triangle] ⇒ ∠DAB + 90° + 90° - x = 180° ⇒ ∠DAB = 180° - 180° + x ⇒ ∠DAB = x. From figure, ∠DAB = ∠CAB = x ∴ ∠CBD = ∠CAB = x (i) cos ∠CBD = cos ∠CAB = . Hence, cos ∠CBD = . (ii) In ∆BCD, ⇒ ∠DBC + ∠DCB + ∠CDB = 180° [Angle sum property of triangle] ⇒ ∠DCB + x + 90° = 180° ⇒ ∠DCB = 180° - 90° - x ⇒ ∠DCB = 90° - x. From figure, ∠DCB = ∠ACB =90° - x ∴ ∠ABD = ∠ACB = 90° - x ∴ cot ∠ABD = cot ∠ACB = . Hence, cot ∠ABD = .

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In figure (1) given below, ∆ABC is right-angled at B and ∆BRS is right-angled at R. If AB = 18 cm, BC = 7.5 cm, RS = 5 cm, ∠BSR = x° and ∠SAB = y°, then find :
(i) tan x°
(ii) sin y°.

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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.

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Mathematics

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

Trigonometrical Ratios

Related Questions

In figure (1) given below, ∆ABC is right-angled at B and ∆BRS is right-angled at R. If AB = 18 cm, BC = 7.5 cm, RS = 5 cm, ∠BSR = x° and ∠SAB = y°, then find :
(i) tan x°
(ii) sin y°.

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.

Mathematics

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

Trigonometrical Ratios

Related Questions

In figure (1) given below, ∆ABC is right-angled at B and ∆BRS is right-angled at R. If AB = 18 cm, BC = 7.5 cm, RS = 5 cm, ∠BSR = x° and ∠SAB = y°, then find :(i) tan x°(ii) sin y°.

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

In figure (1) given below, ∆ABC is right-angled at B and ∆BRS is right-angled at R. If AB = 18 cm, BC = 7.5 cm, RS = 5 cm, ∠BSR = x° and ∠SAB = y°, then find :
(i) tan x°
(ii) sin y°.

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.