Consider a right angled triangle $A B C,$ right angled at $B .$ The length of $A C$ is $5$ cm, the length of $B C$ is $3$ cm and $∠ A = 37^{\circ}$ . The sum of the magnitudes of $A B, B C$ and $∠ C$ is ___

[Magnitude is defined as the absolute value. Example: If $∠ A$ is $60^{\circ}$ then, its magnitude is $60$ ; and if length $A B = 45$ cm, then magnitude of $A B = 45.$ ]

Open in App

Solution

Using angle sum property of a triangle, $∠ A + ∠ B + ∠ C = 180^{\circ}$

$\Rightarrow ∠ C = 180 - ∠ A - ∠ B = 180 - 37 - 90 = 53^{\circ}$

Applying Pythagoras theorem,

$A B^{2} + B C^{2} = A C^{2}$

$\Rightarrow A B^{2} = A C^{2} - B C^{2} = 25 - 9 = 16$ .

$\Rightarrow A B = 4$ cm

Thus, magnitude of $A B, B C$ and $∠ C = 4 + 3 + 53 = 60$

Suggest Corrections

Similar questions

Consider a right angled triangle ABC, right angled at B. Length of AC = 5 cm. $∠$ A = $37^{\circ}$ . The sides of triangles are integers. Then, find the sum of the magnitudes of AB, BC and $∠$ C.

Magnitude is defined as the absolute value. Example: If $∠$ A is 60 degree then, its magnitude is 60; and if length AB = 45 cm, then magnitude of AB = 45.

___

Consider a right angled triangle ABC, right angled at B. Length of AC = 5 cm. $∠$ A = $37^{\circ}$ . The magnitude of the sides of the triangle are natural numbers. Then, the sum of the magnitudes of AB, BC and $∠$ C is ___ .

Magnitude is defined as the absolute value. Example: If $∠$ A is 60 degree then, its magnitude is 60; and if length AB = 45 cm, then magnitude of AB = 45.

Q. In right-angled traingle ABC, ∠B=90∘. Then the magnitude of angle A, if AB is √3 times of BC is

△

ABC is right angled at A. If BC = 60 cm and AC = 61 cm, then find the length of the side AB.

In right-angled triangle

A B C; ∠ B = 90^{\circ}

, then find the magnitude of angle

A

, if AB is

\sqrt{3}

times of

B C

Join BYJU'S Learning Program

Using angle sum property of a triangle, ∠A+∠B+∠C=180∘ ⇒∠C=180−∠A−∠B=180−37−90=53∘ Applying Pythagoras theorem, AB2+BC2=AC2 ⇒AB2=AC2−BC2=25−9=16. ⇒AB=4 cm Thus, magnitude of AB, BC and ∠C=4+3+53=60