Question
Use the 45-45-90 theorem to solve for the hypotenuse.
- 16
- 8
- 8√2
- √16
Hint:
We are given a right-angled triangle. It is 45°-45°-90° triangle. We are given the length of the it’s two sides. We are asked to find the length of its hypotenuse using the 45°-45°-90° theorem. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: 8
Let the given triangle be ABC
∠ABC = 90°
AB = 4√2
BC = 4√2
It is a 45°-45°-90° triangle. The two angles of the triangle are same. It means the sides opposite to the triangle are equal. When a triangle has two sides equal, it is an isosceles triangle.
We are asked the length of the hypotenuse AC.
We have to use the 45°-45°-90° theorem.
The theorem states that, the length of its hypothesis us √2 times the length of its side.
AC = √2(length of the it’s side).
AC = √2 × 4√2
AC = 8
Therefore, the length of the hypotenuse is 8.
For such questions, we should the properties of 45°-45°-90° triangle.
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