Engage NY Eureka Math 8th Grade Module 2 Lesson 15 Answer Key

Example 1.
Now that we know what the Pythagorean theorem is, let’s practice using it to find the length of a hypotenuse of a right triangle.
Determine the length of the hypotenuse of the right triangle. The Pythagorean theorem states that for right triangles a2 +b2 =c2 , where a and b are the legs, and c is the hypotenuse. Then,
a2 +b2 =c2
62 +82 =c2
36+64=c2
100=c2.
Since we know that 100=102, we can say that the hypotenuse c is 10.

Example 2.
Determine the length of the hypotenuse of the right triangle. → Based on our work in the last example, what should we do to find the length of the hypotenuse?
→ Use the Pythagorean theorem, and replace a and b with 3 and 7. Then,
a2 + b2 = c2
32 +72 =c2
9+49=c2
58=c2
→ Since we do not know what number times itself produces 58, for now we can leave our answer as 58=c2 . Later this year, we learn how to determine the actual value for c for problems like this one.

Exercises 1–5
For each of the exercises, determine the length of the hypotenuse of the right triangle shown. Note: Figures are not drawn to scale.

Question 1. a2 +b2 =c2
32 +42 =c2
9+16=c2
25=c2
5=c

Question 2. a2 +b2 =c2
82 +112 =c2
64+121=c2
185=c2

Question 3. a2 +b2 =c2
42 +92 =c2
16+81=c2
97=c2

Question 4. a2 +b2 =c2
22 +52 =c2
4+25=c2
29=c2

Question 5. a2 +b2 =c2
12 +92 =c2
1+81=c2
82=c2

Eureka Math Grade 8 Module 2 Lesson 15 Problem Set Answer Key

Students practice using the Pythagorean theorem to find the length of the hypotenuse of a right triangle.

For each of the problems below, determine the length of the hypotenuse of the right triangle shown. Note: Figures are not drawn to scale.

Question 1. a2 +b2 =c2
32 +92 =c2
9+81=c2
90=c2

Question 2. a2 +b2 =c2
82 +22 =c2
64+4=c2
68=c2

Question 3. a2 +b2 =c2
92 +22 =c2
81+4=c2
85=c2

Question 4. a2 +b2 =c2
72 +12 =c2
49+1=c2
50=c2

Question 5. a2 +b2 =c2
62 +32 =c2
36+9=c2
45=c2

Question 6. a2 +b2 =c2
42 +32 =c2
16+9=c2
25=c2
5=c

Question 7. a2 +b2 =c2
42 +22 =c2
16+4=c2
20=c2

Question 8. a2 +b2 =c2
122 +52 =c2
144+25=c2
169=c2
13=c

Question 9. a2 +b2 =c2
132 +82 =c2
169+64=c2
233=c2

Question 10. a2 +b2 =c2
102 +72 =c2
100+49=c2
149=c2

Question 11. a2 +b2 =c2
122 +92 =c2
144+81=c2
225=c2
15=c

Question 12. a2 +b2 =c2
52 +12 =c2
25+1=c2
26=c2

Eureka Math Grade 8 Module 2 Lesson 15 Exit Ticket Answer Key

Question 1.
Label the sides of the right triangle with leg, leg, and hypotenuse.  Question 2.
Determine the length of c in the triangle shown. a2 +b2 =c2
62 +82 =c2
36+64=c2
100=c2
10=c

Question 3.
Determine the length of c in the triangle shown. 