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A person whose eyes are H = 1.62 m above the floor stands L =2.24m in front of a vertical plane mirror whose bottom edge is 43 cm above the floor. What is the horizontal distance x to the base of the wall supporting the mirror of the nearest point on the floor that can be seen reflected in the mirror?

Draw a line from the person's eyes to the base of the mirror. Next, imagine that to be a ray traveling to the person's eyes, and draw the ray that reflects specularly on the mirror to form that ray. See where it intersects the floor. That is where the nearest point can be seen.

The rays I have described are inclined arctan 0.81/2.24 = 19.9 degrees to horizontal.

I get the distance to be 0.43m*cot 19.9 = 1.19 m

See what you get. You need to draw the figure.

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