In a A B C- - B-35- and - C-55- Write which of the following is true-i A C2-A B2-B C2ii A B2-B C2-A C2iii B C2-A B2-A C2

We have: ∠B = 35° and ∠C = 55° ∴ ∠B = 180 35 55 = 90° nbsp; nbsp; nbsp; (since sum of the angles of any triangle is 180°) We know that the side oppos ...

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Standard VII

Mathematics

Sum of the Lengths of 2 Sides of a Triangle

In a A B C, ∠...

Question

In a ∆ABC, ∠B = 35° and ∠C = 55°. Write which of the following is true:

(i) AC² = AB² + BC²
(ii) AB² = BC² + AC²
(iii) BC² = AB² + AC²

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Solution

We have:
∠B = 35° and ∠C = 55°

∴ ∠B = 180 - 35 -55 = 90° (since sum of the angles of any triangle is 180°)

We know that the side opposite to the right angle is the hypotenuse.

By Pythagoras theorem:
BC² = AB² + AC²

Hence, (iii) is true.

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In a ∆ABC, ∠B = 35° and ∠C = 55°. Write which of the following is true: (i) AC2 = AB2 + BC2 (ii) AB2 = BC2 + AC2 (iii) BC2 = AB2 + AC2

We have: ∠B = 35° and ∠C = 55° ∴ ∠B = 180 - 35 -55 = 90° (since sum of the angles of any triangle is 180°) We know that the side opposite to the right angle is the hypotenuse. By Pythagoras theorem: BC2 = AB2 + AC2 Hence, (iii) is true.

In a ∆ABC, ∠B = 35° and ∠C = 55°. Write which of the following is true:

(i) AC² = AB² + BC²
(ii) AB² = BC² + AC²
(iii) BC² = AB² + AC²

We have:
∠B = 35° and ∠C = 55°

∴ ∠B = 180 - 35 -55 = 90° (since sum of the angles of any triangle is 180°)

We know that the side opposite to the right angle is the hypotenuse.

By Pythagoras theorem:
BC² = AB² + AC²

Hence, (iii) is true.