Math Problem Statement
Solution
Let's solve the problems in the given image step by step.
Problem (a)
For the first triangle, we have:
- It is a 45°-45°-90° triangle.
- One leg is 3 units, and we need to find the hypotenuse .
In a 45°-45°-90° triangle, the hypotenuse is times the length of each leg. So:
So, .
Problem (b)
For the second triangle, we have:
- It is a 30°-60°-90° triangle.
- The side opposite the 30° angle is 4 units, and we need to find the hypotenuse .
In a 30°-60°-90° triangle, the hypotenuse is twice the length of the side opposite the 30° angle. So:
So, .
Answers
(a)
(b)
Would you like more details or have any questions?
Here are some related questions:
- How do you determine the hypotenuse in a 45°-45°-90° triangle if only one leg is given?
- What is the relationship between the sides of a 30°-60°-90° triangle?
- How can the Pythagorean theorem be applied to find missing sides in right triangles?
- How do you round answers to the nearest tenth in mathematical calculations?
- What are the other common special right triangles and their properties?
Tip: For 45°-45°-90° triangles, remember the sides have a ratio of 1:1:√2, and for 30°-60°-90° triangles, the ratio is 1:√3:2.
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Math Problem Analysis
Mathematical Concepts
Geometry
Trigonometry
Formulas
Hypotenuse in 45°-45°-90° triangle: d = leg × √2
Hypotenuse in 30°-60°-90° triangle: a = side opposite 30° × 2
Theorems
Pythagorean theorem
Suitable Grade Level
High School
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