Question

1. what is the ratio of the sides for triangle xyc?

1:2:√3
1:1:√3
1:1:√2
1:2:√2

Explanation:

Step1: Identify triangle type

Triangle \( XYC \) has \( \angle XYC = 90^\circ \) (right angle) and \( \angle XCY = 45^\circ \). So the third angle \( \angle CXY = 180^\circ - 90^\circ - 45^\circ = 45^\circ \). Thus, it's an isosceles right triangle.

Step2: Recall isosceles right triangle side ratio

In an isosceles right triangle (angles \( 45^\circ - 45^\circ - 90^\circ \)), the ratio of the legs (equal sides) to the hypotenuse is \( 1:1:\sqrt{2} \) (since if legs are length \( a \), hypotenuse \( c = a\sqrt{2} \) by Pythagoras: \( c^2 = a^2 + a^2 = 2a^2 \Rightarrow c = a\sqrt{2} \)).

Answer:

\( 1:1:\sqrt{2} \) (the option with this ratio)