Find the hypotenuse of a right triangle with one leg of length 4sqrt(2) cm and angl...
Check the final answer first, then review the worked steps.
Problem
Find the hypotenuse of a right triangle with one leg of length 4*sqrt(2) cm and angles 45, 45, 90 degrees.
Answer
8 cm
Step-by-step solution
- Identify the triangle type: The image shows a triangle with angles $45^\circ$, $45^\circ$, and a right angle ($90^\circ$). This is a special type of right triangle known as a 45-45-90 triangle, which is also an isosceles triangle.
- Recall properties of a 45-45-90 triangle: In a 45-45-90 triangle, the two legs are equal in length, and the hypotenuse is $\sqrt{2}$ times the length of a leg.
- Identify the given information: The length of one leg is given as $4\sqrt{2}$ cm. Since it's a 45-45-90 triangle, the other leg is also $4\sqrt{2}$ cm. The side labeled 'z' is the hypotenuse.
- Calculate the hypotenuse (z): Using the property that the hypotenuse is $\sqrt{2}$ times the length of a leg, we can write the equation: $$z = (\text{leg length}) \times \sqrt{2}$$ $$z = (4\sqrt{2} \text{ cm}) \times \sqrt{2}$$
- Simplify the expression: $$z = 4 \times (\sqrt{2} \times \sqrt{2}) \text{ cm}$$ $$z = 4 \times 2 \text{ cm}$$ $$z = 8 \text{ cm}$$