Answer:
x=5 cm
Step-by-step explanation:
triangle ABC is an isoceles triangle
so BC=AC and angle A=angle B
BC=X and angle A=theta
angle B and angle A both is theta degree because base angles of an isosceles triangle are equal
to find angle A and B
angle A + angle B + angle c=180 degree (sum of interior angles of a triangle)
theta + theta +90=180
2theta=180-90
2theta=90
theta=90/2
theta=45 degree
sin both angle A and angle B are theta their value is 45 degree.
For side x
now using pythagoras theorem
take theta as reference angle
using sin rule
sin 45=opposite/hypotenuse
[tex]\frac{1}{\sqrt{2} }[/tex] =x/[tex]5\sqrt{2}[/tex]
[tex]\frac{1}{\sqrt{2} } *5\sqrt{2}[/tex]=x
[tex]\frac{5\sqrt{2} }{\sqrt{2} } }[/tex]=x
5=x
