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

₹0.0

Question: In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the length of side XY if side XZ = 10 cm? (2020)

Options:

Correct Answer: 5√2 cm

Exam Year: 2020

Solution:

In an isosceles right triangle, the sides opposite the 45-degree angles are equal. Therefore, XY = XZ / √2 = 10 / √2 = 5√2 cm.

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the length of side XY if side XZ = 10 cm? (2020)

In triangle XYZ, if angle X = 45 degrees and angle Y = 45 degrees, what is the length of side XY if side XZ = 10 cm? (2020)

Step 1: Identify the type of triangle. Since angle X and angle Y are both 45 degrees, triangle XYZ is an isosceles right triangle.
Step 2: Understand that in an isosceles right triangle, the two sides opposite the 45-degree angles are equal in length.
Step 3: Recognize that side XZ is given as 10 cm. This side is opposite the 90-degree angle.
Step 4: Use the property of isosceles right triangles: the length of the sides opposite the 45-degree angles (XY and YZ) can be found using the formula: side = hypotenuse / √2.
Step 5: Substitute the value of side XZ into the formula: XY = XZ / √2 = 10 cm / √2.
Step 6: Simplify the expression: XY = 10 / √2 = 10√2 / 2 = 5√2 cm.

Isosceles Right Triangle Properties – In an isosceles right triangle, the angles are 45-45-90 degrees, and the sides opposite the equal angles are equal, with the relationship between the hypotenuse and the legs being leg = hypotenuse / √2.