Question

1. for each set of possible triangle side lengths, determine if the side lengths form a right triangle. drag and drop each set into the appropriate category

side lengths form a right triangle
side lengths do not form a right triangle
:: 1.3, 8.4, 8.5
:: 4, 8.5, 9.25
:: 15, 55.25, 57.25
:: 1.5, 2, 2.5
:: 3.8, 36, 36.2

1. a pendant flag is made up of a stick and a triangular flag, as shown in the diagram below. what is h, the total height in inches of the stick?

Explanation:

For each set, use the Pythagorean theorem: $a^2 + b^2 = c^2$, where $c$ is the longest side.

Step1: Test 1.3, 8.4, 8.5

Calculate $1.3^2 + 8.4^2 = 1.69 + 70.56 = 72.25$; $8.5^2 = 72.25$

Step2: Test 4, 8.5, 9.25

Calculate $4^2 + 8.5^2 = 16 + 72.25 = 88.25$; $9.25^2 = 85.5625$

Step3: Test 15, 55.25, 57.25

Calculate $15^2 + 55.25^2 = 225 + 3052.5625 = 3277.5625$; $57.25^2 = 3277.5625$

Step4: Test 1.5, 2, 2.5

Calculate $1.5^2 + 2^2 = 2.25 + 4 = 6.25$; $2.5^2 = 6.25$

Step5: Test 3.8, 36, 36.2

Calculate $3.8^2 + 36^2 = 14.44 + 1296 = 1310.44$; $36.2^2 = 1310.44$

Answer:

Side lengths form a right triangle:

1.3, 8.4, 8.5
15, 55.25, 57.25
1.5, 2, 2.5
3.8, 36, 36.2

Side lengths do NOT form a right triangle:

4, 8.5, 9.25

Note: For question 6, the diagram is missing, so the height of the stick cannot be calculated. Please provide the diagram or additional details for question 6.