Answer: 1. Route ABC is a right triangle.
2. Route CDE ia not a right triangle.
3. Distance HJ= 23.32miles
4. Distance GE = 17
5. Missing length= 35
6. The sides 16, 60, 62 do NOT belong to a right triangle.
Step-by-step explanation:
Going by Pythagoras theorem, for triangle to be proven to be a right triangle, the condition below must be satisfied.
Hypotenuse² = Opposite² + Adjacent²
For question 1,
Hyp =13, opp = 5, Adj is 12
Going by Pythagoras rule.
Since 13²= 5² + 12²
Then triangle ABC is a right triangle.
For question 2,
Using the same Pythagoras theorem to prove,
In triangle CDE,
Hyp= 22, opp= 18, Adj = 14
Since 22² is not = 18² + 14²
then CDE is not a right triangle.
For question 3,
For triangle HIJ, since it is confirmed to be a right triangle, then we use the Pythagoras theorem to calculate the missing side.
Longest side if the triangle= IJ = hypotenuse = 25
HI = 9.
IJ² = HI² + HJ²
HJ²= IJ² - HI²
HJ² = 25² - 9²
HJ² = 625 - 81
HJ= √544
HJ = 23.32miles
For question 4,
FGE is also shown to be a right triangle and the missing side GE is the longest side which is also the hypotenuse.
FG= 8, FE =15
Using the Pythagoras theorem,
Hyp² = FG² + FE²
GE² = 8² + 15²
GE² = 289
GE = √289
GE = 17.
For question 5,
The hypotenuse is given as 37, one side is given as 12, let's call the missing side x
Going by Pythagoras theorem,
37² = 12²+ x²
x²= 37² - 12²
x²= 1225
x=√1225
x=35.
The missing side is 35inches.
For number 6,
The numbers given are 16, 60, 62
To know if three sides belong to a right angle, we simply put them to test using Pythagoras theorem.
It is worthy of note that the longest side is the hypotenuse.
This brings us to the equation to check below that since:
62² Is not = 60² + 16²
Then the side lengths 16, 60, 62 do not belong to a right angle.
