In a triangle, if one angle is 90 degrees and the other two angles are 45 degree

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Question: In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the legs are 5 cm each?

Options:

Correct Answer: 12.5 cm²

Solution:

Area = 1/2 * base * height = 1/2 * 5 * 5 = 12.5 cm².

In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the legs are 5 cm each?

In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the legs are 5 cm each?

Step 1: Identify the type of triangle. Since one angle is 90 degrees and the other two angles are 45 degrees each, this is a right triangle (specifically, an isosceles right triangle).
Step 2: Understand the legs of the triangle. The legs are the two sides that form the right angle. In this case, both legs are 5 cm each.
Step 3: Use the formula for the area of a triangle. The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.
Step 4: Assign the base and height. In a right triangle, the two legs can be considered as the base and height. Here, both the base and height are 5 cm.
Step 5: Plug the values into the area formula. Substitute the base and height into the formula: Area = 1/2 * 5 * 5.
Step 6: Calculate the area. First, multiply 5 by 5 to get 25. Then, multiply 25 by 1/2 to get 12.5.
Step 7: State the final area. The area of the triangle is 12.5 cm².

Triangle Area Calculation – Understanding how to calculate the area of a right triangle using the formula Area = 1/2 * base * height.
Properties of Right Triangles – Recognizing that in a right triangle with angles of 45 degrees, the legs are equal in length.