Answer:
x=5
Step-by-step explanation:
triangle ABC is an is0sceles triangle because according to the figur it's two sides are equal.
angle B = angle (because base angles of an isosceles triangle are equal)
so let angle A also be theta
now lets find the value of theta
angle A + angle B + angle C =10 degree (sum of interior angles of a triangle)
theta + theta +90 =180
2 theta =180-90
theta =90/2
theta =45 degree
therefore the value of theta is 45 degree.
so angle A =45 degree and angle B =45 degree
to find x
Take angle B as reference angle
using sin rule
sin 45 = opposite/hypotenuse
[tex]\frac{1}{\sqrt{2} } =\frac{x}{5\sqrt{2} }[/tex]
do cross multiplication
[tex]x * \sqrt{2 } = 5\sqrt{2} *1[/tex]
[tex]x = \frac{5\sqrt{2} }{\sqrt{2} }[/tex] (root 2 and root 2 gets cancel)
[tex]x=5[/tex]
