Podcast
Questions and Answers
In a right triangle, which side is always the longest?
In a right triangle, which side is always the longest?
- The hypotenuse (correct)
- The angle side
- The adjacent side
- One of the legs
If a triangle has angles measuring 60° and 30°, what type of triangle is it?
If a triangle has angles measuring 60° and 30°, what type of triangle is it?
- Equilateral triangle
- Acute triangle
- Right triangle (correct)
- Obtuse triangle
If the legs of a right triangle are 3 and x and the hypotenuse is 5, what is the value of x?
If the legs of a right triangle are 3 and x and the hypotenuse is 5, what is the value of x?
- 3.5
- 5
- 4 (correct)
- 2
What is the rise of a road with a 7% grade for a run of 100ft?
What is the rise of a road with a 7% grade for a run of 100ft?
What is the length of a ladder needed to reach a window 12 ft above ground using a 4:1 vertical to horizontal ratio?
What is the length of a ladder needed to reach a window 12 ft above ground using a 4:1 vertical to horizontal ratio?
For a triangle with sides of lengths 1, 2, and 3, which statement is correct?
For a triangle with sides of lengths 1, 2, and 3, which statement is correct?
What is the relationship between the angles and sides in any triangle?
What is the relationship between the angles and sides in any triangle?
In a right triangle, if one angle is 70°, what can be said about the other two angles?
In a right triangle, if one angle is 70°, what can be said about the other two angles?
Flashcards
Right Triangle
Right Triangle
A triangle with one 90-degree angle.
Hypotenuse
Hypotenuse
The longest side of a right triangle, opposite the right angle.
Legs
Legs
The two shorter sides of a right triangle.
Pythagorean Theorem
Pythagorean Theorem
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Grade
Grade
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Right Angle
Right Angle
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7% Grade (Example)
7% Grade (Example)
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25% Grade Example
25% Grade Example
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Study Notes
Pythagorean Theorem
- A 90° angle is a right angle.
- A right triangle has a 90° angle.
- The side opposite the 90° angle is the hypotenuse.
- The other two sides are the legs.
- The angles in any triangle add up to 180°.
- The longest side is opposite the largest angle; the shortest side is opposite the smallest angle.
- In a right triangle, the hypotenuse is the longest side.
- a² = b² + c² (formula relating sides of a right triangle)
Exercise 1
- Question 1: Given angles 60° and 30° in a triangle, is it a right triangle? No.
- Question 2: A triangle with a 100° angle is it a right triangle? No.
- Question 3: A triangle with a 70° angle is it a right triangle? Maybe.
- Question 4: Legs of a right triangle are 3 and x, hypotenuse is 5. Find x. x = 4
- Question 5: Triangle side lengths 1, 3, and 2. Is it a right triangle? No.
Exercise 2
- Question 1: A 12 ft high window, 4:1 vertical to horizontal ratio for a ladder. What is the length of the ladder? 12.37 ft
- Question 2: Triangle with sides A,B, and C (C=19, A=x, B=3x). Find A and B. A=6.01, B=18.03
- Question 3: (Figure with iterative side lengths). Find X6. X6 = 2.65
- Question 4: A 3 ft high truck bed ramp with a 25% grade. How long is the ramp? 12.37 ft
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