Special Right Triangles Homework

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| By Annacabral

Annacabral

Community Contributor

Quizzes Created: 29 | Total Attempts: 18,962

Questions: 8 | Attempts: 479 | Updated: Mar 21, 2023

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Mathematicians and all mathematics students who are almost doing their exams and need practice, this quiz is for you. Get ready for your knowledge to be tested on various special right triangle questions.

Questions and Answers

1.

Find the missing side of the 45-45-90 triangle.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
C. C

Explanation
In a 45-45-90 triangle, the two legs are congruent, meaning they have the same length. Therefore, if side A and side B are the two legs, and side C is the missing side, it must also be equal in length to sides A and B. Hence, the missing side of the triangle is C.

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2.

Find the missing side of the 45-45-90 triangle.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
B. B
3.

Find the missing side of the 45-45-90 triangle.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
E. E
4.

Find the missing side of the 30-60-90 triangle.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
B. B
5.

Find the missing side of the 30-60-90 triangle below.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
D. D

Explanation
In a 30-60-90 triangle, the sides are in the ratio of 1:√3:2. Since side D is the longest side, it corresponds to the hypotenuse, which is twice the length of the shortest side. Therefore, side D is twice the length of side A.

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6.

Find the missing side of the 30-60-90 triangle below.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
D. D
7.

You have created a house with a deck of cards and the roof is an isosceles right triangle. The cards are 4 inches long (the sides of your roof). What is the width of your roof (the hypotenuse of the triangle) approximately?
- A.
  
  2.9 inches
- B.
  
  5.6 inches
- C.
  
  6.8 inches
- D.
  
  8 inches
- E.
  
  Not enough information
Correct Answer
B. 5.6 inches

Explanation
The width of the roof, which is the hypotenuse of the isosceles right triangle, can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the other two sides are both 4 inches long. By substituting these values into the equation, we can solve for the hypotenuse. The approximate width of the roof, therefore, is 5.6 inches.

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8.

Find the altitude (the height) of an equilateral triangle that has sides equal to 12 units.
- A.
  
  A
- B.
  
  B
- C.
  
  C
- D.
  
  D
- E.
  
  E
Correct Answer
C. C

Explanation
To find the altitude of an equilateral triangle, we can use the formula h = (√3/2) * s, where h is the height and s is the length of the side. In this case, the length of the side is given as 12 units. Plugging this value into the formula, we get h = (√3/2) * 12. Simplifying further, h = (√3/2) * 12 = (√3) * 6 = 6√3 units. Therefore, the altitude of the equilateral triangle is 6√3 units.

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