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In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the r

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Question: In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)

Options:

  1. 1:1
  2. 1:√2
  3. √2:1
  4. 2:1

Correct Answer: 1:1

Exam Year: 2021

Solution: 

In an isosceles triangle with angles 45 degrees, the sides opposite these angles are equal, hence the ratio is 1:1.

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the r

Practice Questions

Q1
In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)
  1. 1:1
  2. 1:√2
  3. √2:1
  4. 2:1

Questions & Step-by-Step Solutions

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the ratio of the lengths of sides opposite to these angles? (2021)
  • Step 1: Identify the triangle XYZ and the given angles. We have angle X = 45 degrees and angle Y = 45 degrees.
  • Step 2: Recognize that in a triangle, the sum of all angles is 180 degrees. Since angle X and angle Y are both 45 degrees, we can find angle Z.
  • Step 3: Calculate angle Z: 180 degrees - (45 degrees + 45 degrees) = 90 degrees. So, angle Z = 90 degrees.
  • Step 4: Note that triangle XYZ has two angles that are equal (45 degrees each), which makes it an isosceles triangle.
  • Step 5: In an isosceles triangle, the sides opposite the equal angles are also equal in length.
  • Step 6: Since the sides opposite angle X and angle Y are equal, the ratio of their lengths is 1:1.
  • Triangle Properties – Understanding the properties of isosceles triangles, particularly that angles opposite equal sides are equal.
  • Angle Sum Property – Applying the angle sum property of triangles to deduce the third angle when two angles are known.
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