(Please answer all of the 5 questions. )
1. What is the value of x in this right triangle?
A. 6
B. 8
C. 16
D. 18
2. The figure above/below is a right triangle. A balloon is at the end of a string that is 60 feet in length. The ground distance from the person to the balloon is 50 feet. What is the altitude of the balloon to the nearest tenth?
A. 3.2 feet
B. 10.5 feet
C. 33.2 feet
D. 78.1
3. If a triangle has sides of lengths a, b, and c, and a^2 + b^2= c^2, then the triangle is a right triangle. Let b=84 units and let c=85 units, as shown.
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What is the value for a that completes the set of three numbers that can be the side lengths of a right triangle?
(There is no answer choice for 3 so you have to solve it.)
4. James wants to informally prove the converse of the Pythagorean Theorem by producing some evidence that supports it.
Recall that the converse of the Pythagorean Theorem states:
If a triangle has side lengths a, b, c, such that a^2 + b^2 = c^2, then the triangle is a right triangle.
James is going to construct several triangles with different side lengths. Select/Choose the TWO true statements that James can use as evidence to support the converse of the Pythagorean Theorem.
A. A triangle with side lengths measuring 15, 18, and 21 units is a right triangle.
B. A triangle with side lengths measuring 15, 20, and 25 units is a right triangle.
C. A triangle with side lengths measuring 16, 20 and 24 units is a right triangle.
D. A triangle with side lengths measuring 16, 30, and 34 units is a right triangle.
5. Which of the following sets of lengths can Sean use to make a right triangle?
Group of answer choices
A. {5 cm, 15 cm, 18 cm}
B. {6 cm, 12 cm, 16 cm}
C. {5 cm, 13 cm, 15 cm}
D. {8 cm, 15 cm, 17 cm}
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Answers
Answered by
2
Answer:
1. 16
2. 33.2
3. 13
4. B and C
5. D
Answered by
2
Solved all 5 based on Pythagorean Theorem
Step-by-step explanation:
1. What is the value of x in this right triangle?
applying pythagorus theorem
x² = 20² - 12²
=> x² = 400 - 144
=> x² = 256
=> x = 16
2. altitude of the balloon = x
x² = 60² - 50²
=> x² = 3600 - 2500
=> x² = 1100
=> x = 10√11
=> x = 33.2 feet
3. a² +b² = c²
a² + 84² = 85²
=> a² = 169
=> a = 13
4, A triangle with side lengths measuring 15, 20, and 25 units is a right triangle.
as 15² + 20² = 25²
5.
D. {8 cm, 15 cm, 17 cm} can be used to make right angle triangle
as 15² + 8² = 17²
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