How do you solve a 45 45 90 triangle calculator?
The Correct Answer and Explanation is :
A 45-45-90 triangle is an isosceles right triangle where both non-hypotenuse sides are congruent, and the angles are 45°, 45°, and 90°. This type of triangle has special properties that make it easy to solve with a simple formula.
Properties of a 45-45-90 Triangle
- The two legs are of equal length.
- The hypotenuse is ( \sqrt{2} ) times the length of a leg.
If one leg is given, you can use these properties to find the other leg and the hypotenuse:
- Legs (a): If the length of one leg is (a), then the length of the other leg is also (a).
- Hypotenuse (c): The hypotenuse (c) is (a\sqrt{2}), where (a) is the length of either leg.
How to Solve a 45-45-90 Triangle
- Given the length of a leg: If you’re given one leg, say (a), you can find the other leg and the hypotenuse.
- The second leg is the same as the first, so the second leg is also (a).
- The hypotenuse is (a\sqrt{2}).
- Given the length of the hypotenuse: If you’re given the hypotenuse, say (c), you can find the length of the legs.
- To find each leg, use the formula (a = \frac{c}{\sqrt{2}}).
Example Problem
If a 45-45-90 triangle has legs of length 5 units:
- The second leg is also 5 units.
- The hypotenuse is (5\sqrt{2} \approx 7.07) units.
Using a Calculator
- For Leg to Hypotenuse: If you know the leg and need the hypotenuse, multiply the leg length by ( \sqrt{2} ). On a calculator, this would be:
[
\text{Hypotenuse} = \text{Leg} \times \sqrt{2}
] - For Hypotenuse to Leg: If you know the hypotenuse and need the leg, divide the hypotenuse by ( \sqrt{2} ):
[
\text{Leg} = \frac{\text{Hypotenuse}}{\sqrt{2}}
]
In summary, solving a 45-45-90 triangle is straightforward by applying the known ratios between the legs and the hypotenuse. Using a calculator simplifies the process when working with square roots.