Special Right Triangles Homework

1. Find the missing side of the 45-45-90 triangle.

A

B

C

D

E

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.

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.

2. Find the missing side of the 45-45-90 triangle.

A

B

C

D

E

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Explanation

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3. Find the missing side of the 30-60-90 triangle below.

A

B

C

D

E

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Explanation

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4. Find the missing side of the 30-60-90 triangle below.

A

B

C

D

E

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.

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.

5. Find the missing side of the 45-45-90 triangle.

A

B

C

D

E

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Explanation

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6. Find the missing side of the 30-60-90 triangle.

A

B

C

D

E

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Explanation

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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?

2.9 inches

5.6 inches

6.8 inches

8 inches

Not enough information

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.

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.

8. Find the altitude (the height) of an equilateral triangle that has sides equal to 12 units.

A

B

C

D

E

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.

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.