Question

If ∆ ABC ,seg AD perpendicular to seg BC;angle C=45°,BD =5 and AC=8√2 then find AD​

Answer 1

AD = 8 and BC = 13

Step-by-step explanation:

given AD is perpendicular to BC

=> ∠D = 90°

now consider Δle ADC

here ∠D is 90° and ∠C is 45°

sum of angles equals to 180° so, ∠A = 45°

when two angles are equal it is a isosceles triangle in which two sides are also equal

so AD = DC

hypotenuse theorem, AC² = DC² + AD²

=> (8√2)² = 2DC²

=> 128/2 = DC²

=> DC = 8 =AD

so AD = 8 then

BC = BD + DC

=> BC = 13

i hope it's helpful to you ... !!!