In triangle GHI, if angle G is 45 degrees and side GH is 5 cm, what is the lengt

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Question: In triangle GHI, if angle G is 45 degrees and side GH is 5 cm, what is the length of side HI if triangle GHI is a right triangle?

Options:

Correct Answer: 5√2 cm

Solution:

In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal, so HI = GH√2 = 5√2 cm.

In triangle GHI, if angle G is 45 degrees and side GH is 5 cm, what is the length of side HI if triangle GHI is a right triangle?

In triangle GHI, if angle G is 45 degrees and side GH is 5 cm, what is the length of side HI if triangle GHI is a right triangle?

Step 1: Identify that triangle GHI is a right triangle with angle G equal to 45 degrees.
Step 2: Recognize that in a right triangle with a 45-degree angle, the other angle must also be 45 degrees (since the angles in a triangle add up to 180 degrees).
Step 3: Understand that this means triangle GHI is a 45-45-90 triangle.
Step 4: In a 45-45-90 triangle, the sides opposite the 45-degree angles are equal.
Step 5: Since side GH is 5 cm, side HI must also be 5 cm because they are opposite the 45-degree angles.
Step 6: To find the length of the hypotenuse (side GI), use the formula: hypotenuse = side × √2.
Step 7: Calculate the length of side GI: GI = 5 cm × √2.
Step 8: Therefore, the length of side HI is 5√2 cm.

Properties of 45-45-90 Triangles – In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is the leg length multiplied by √2.
Right Triangle Relationships – Understanding the relationships between angles and sides in right triangles, particularly the special properties of 45-45-90 triangles.