If $△$ ABC is a right angled triangle with $∠$ B = 90°, AB = 15 units and BC = 112 units, find its third side ___.

Open in App

Solution

By Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since in this triangle, the third side is the side opposite to the right angle and hence is the hypotenuse, we must have,
$\Rightarrow$ $A C^{2} = 15^{2} + 112^{2}$
$\Rightarrow A C = \sqrt{12769} = 113$ units

Suggest Corrections

Similar questions

Q. In a right triangle ABC, right angled at C, if ∠B = 60° and AB = 15 units. Find the remaining angles and sides.

Q. If

Δ A B C

is a right triangle such that

∠ C = 90^{\circ}, ∠ A = 45^{\circ}

and

B C = 7

units. Find

∠ B, A B

and

A C

In triangle ABC, right angled at B, if $∠$ A is made larger and larger till it becomes $90^{\circ}$ , what can you say about AC and AB if BC = 1 unit?

A B C

is a right-angled triangle, right-angled at

B

/. Given that

∠ A C B = θ

, side

A B = 2

units and side

B C = 1 u n i t

, find the value of

{sin}^{2} θ + {tan}^{2} θ

Q. In a right

△ ABC

, right angled at

C

, if

∠ B = 60^{\circ}

and

AB = 15

units. Find the remaining angles and sides.

Join BYJU'S Learning Program

If △ABC is a right angled triangle with ∠B = 90°, AB = 15 units and BC = 112 units, find its third side ___.

By Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Since in this triangle, the third side is the side opposite to the right angle and hence is the hypotenuse, we must have, ​⇒ AC2=152+1122 ⇒AC=√12769=113 units

If $△$ ABC is a right angled triangle with $∠$ B = 90°, AB = 15 units and BC = 112 units, find its third side ___.