Question

find the area of triangle ABC in which angle abc is equals to 90 degree angle ACB is equal to 45 degree and ac is equals to 8 centimetre​

Answer 1

Step-by-step explanation:

Answer in this pic ❤❤

Answer is 16 cm'2

Answer 2

given :

$\angle B = 90^\circ \\\\\angle C = 45^\circ\\\\AC = 8 cm$

To find : area of triangle ABC

solution :

using the angle sum property

$\angle A + \angle B + \angle C = 180^\circ \\\\\angle A = 180-(90+45) \\\\\angle A = 45^\circ \\\\\angle A = \angle C = 45^\circ$

thus BC = AB (side opposite to equal angle are equal )

thus , ABC  is a isosceles triangle

let

BC = AB = x

then using Pythagoras theorem

AC² = AB² + BC²

8² = x² + x²

64 = 2x²

x² = 32

x = 4√2

then area of triangle ABC

$\frac{1}{2} \times base \times height \\\\\frac{1}{2} \times BC \times AB \\\\\frac{1}{2} \times 4\sqrt{2} \times 4\sqrt{2} \\\\= 16 cm ^2$

hence , The area of triangle ABC is 16 cm ²