Question

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Answer 1

The two triangles are similar by the AA Similarity theorem.

The height of the tree can be calculated by figuring out the ratio between the distance between the mirror to her feet and the distance from the mirror to the tree

How to use the concept of similar Triangles?

From Law of Reflection, we know that the angle of incidence and the angle of reflection are equal to each other.

Now, triangles can be proved similar by the AA, SAS, or SSS theorems. However, in this question, the triangles as seen in the attached image can be proved similar by the AA similarity theorem.

This is because both triangles have one congruent angle in common.

Sarah and the tree are standing straight and perpendicular to the ground and as such, the angles formed by Sarah and the tree are right angles.

The above tells us that the two triangles have two angles in common, making them similar triangles by the AA (Angle Angle) similarity theorem.

Since the triangles are similar, it means that the ratios of the sides of the triangles will be the same. Thus,  if Sarah knows the distance from the mirror to her feet and the distance from the mirror to the tree, she can create the ratio between the two triangles.

Read more about Similar Triangles at; brainly.com/question/14285697

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