In the given figure; BC = 15 cm and sin B 4/5 . (i) Calculate the measures of AB and AC. (ii) Now, if tan ∠ADC = 1; calculate the measures of CD and AD.

Question

KnowledgeBoat · Accepted Answer

(i) Given: ∴ If length of AC = 4x cm, length of AB = 5x cm. In Δ ABC, ⇒ AB2= BC2 \+ AC2 (∵ AB is hypotenuse) ⇒ (5x)2 = BC2 \+ (4x)2 ⇒ 25x2 = BC2 \+ 16x2 ⇒ BC2 = 25x2 \- 16x2 ⇒ BC2 = 9x2 ⇒ BC = ⇒ BC = 3x It is given that BC = 15 cm 3x = 15 x = x = 5 cm AB = 5x = 5 x 5 cm = 25 cm AC = 4x = 4 x 5 cm = 20 cm Hence, AB = 25 cm and AC = 20 cm. (ii) tan ∠ADC = 1 ∴ If length of AC = x unit, length of CD = x unit. From (i), we know AC = 20 cm ∴ x = 20 cm So, AC = CD = 20 cm In Δ ACD, ⇒ AD2 = AC2 \+ CD2 (∵ AD is hypotenuse) ⇒ AD2 = 202 \+ 202 ⇒ AD2 = 400 \+ 400 ⇒ AD2 = 800 ⇒ AD = ⇒ AD = Hence, CD = 20 cm and AD = 20 cm.

Mathematics

In the given figure; BC = 15 cm and sin B 4/5 . (i) Calculate the measures of AB and AC. (ii) Now, if tan ∠ADC = 1; calculate the measures of CD and AD.

Trigonometric Identities

Related Questions

Using the measurements given in the following figure :
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If sin A + cosec A = 2; find the value of sin² A + cosec² A.

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Mathematics

In the given figure; BC = 15 cm and sin B 4/5 . (i) Calculate the measures of AB and AC. (ii) Now, if tan ∠ADC = 1; calculate the measures of CD and AD.

Trigonometric Identities

Related Questions

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.

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

If tan A + cot A = 5; find the value of tan2 A + cot2 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.

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

If tan A + cot A = 5; find the value of tan² A + cot² A.