In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the l

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Question: In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the length of side DE if DF = 10 cm? (2023)

Options:

Correct Answer: 5√2 cm

Exam Year: 2023

Solution:

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

In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the length of side DE if DF = 10 cm? (2023)

In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the length of side DE if DF = 10 cm? (2023)

Step 1: Identify the type of triangle. Since angle D and angle E are both 45 degrees, triangle DEF is an isosceles right triangle.
Step 2: Understand that in an isosceles right triangle, the sides opposite the 45-degree angles are equal. This means DE is equal to DF.
Step 3: Use the relationship between the sides in an isosceles right triangle. The side opposite the right angle (DF) is equal to the length of one of the other sides (DE) multiplied by √2.
Step 4: Rearrange the formula to find DE. DE = DF / √2.
Step 5: Substitute the value of DF into the formula. DE = 10 cm / √2.
Step 6: Simplify the expression. DE = 10/√2 cm, which can be further simplified to 5√2 cm.

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