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

### Eureka Math Grade 8 Module 2 Lesson 15 Example 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 a^{2} +b^{2} =c^{2} , where a and b are the legs, and c is the hypotenuse. Then,

a^{2} +b^{2} =c^{2}

6^{2} +8^{2} =c^{2}

36+64=c^{2}

100=c^{2}.

Since we know that 100=10^{2}, 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,

a^{2} + b^{2} = c^{2}

3^{2} +7^{2} =c^{2}

9+49=c^{2}

58=c^{2}

→ Since we do not know what number times itself produces 58, for now we can leave our answer as 58=c^{2} . Later this year, we learn how to determine the actual value for c for problems like this one.

### Eureka Math Grade 8 Module 2 Lesson 15 Exercise Answer Key

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.

Answer:

a^{2} +b^{2} =c^{2}

3^{2} +4^{2} =c^{2}

9+16=c^{2}

25=c^{2}

5=c

Question 2.

Answer:

a^{2} +b^{2} =c^{2}

8^{2} +11^{2} =c^{2}

64+121=c^{2}

185=c^{2}

Question 3.

Answer:

a^{2} +b^{2} =c^{2}

4^{2} +9^{2} =c^{2}

16+81=c^{2}

97=c^{2}

Question 4.

Answer:

a^{2} +b^{2} =c^{2}

2^{2} +5^{2} =c^{2}

4+25=c^{2}

29=c^{2}

Question 5.

Answer:

a^{2} +b^{2} =c^{2}

1^{2} +9^{2} =c^{2}

1+81=c^{2}

82=c^{2}

### 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.

Answer:

a^{2} +b^{2} =c^{2}

3^{2} +9^{2} =c^{2}

9+81=c^{2}

90=c^{2}

Question 2.

Answer:

a^{2} +b^{2} =c^{2}

8^{2} +2^{2} =c^{2}

64+4=c^{2}

68=c^{2}

Question 3.

Answer:

a^{2} +b^{2} =c^{2}

9^{2} +2^{2} =c^{2}

81+4=c^{2}

85=c^{2}

Question 4.

Answer:

a^{2} +b^{2} =c^{2}

7^{2} +1^{2} =c^{2}

49+1=c^{2}

50=c^{2}

Question 5.

Answer:

a^{2} +b^{2} =c^{2}

6^{2} +3^{2} =c^{2}

36+9=c^{2}

45=c^{2}

Question 6.

Answer:

a^{2} +b^{2} =c^{2}

4^{2} +3^{2} =c^{2}

16+9=c^{2}

25=c^{2}

5=c

Question 7.

Answer:

a^{2} +b^{2} =c^{2}

4^{2} +2^{2} =c^{2}

16+4=c^{2}

20=c^{2}

Question 8.

Answer:

a^{2} +b^{2} =c^{2}

12^{2} +5^{2} =c^{2}

144+25=c^{2}

169=c^{2}

13=c

Question 9.

Answer:

a^{2} +b^{2} =c^{2}

13^{2} +8^{2} =c^{2}

169+64=c^{2}

233=c^{2}

Question 10.

Answer:

a^{2} +b^{2} =c^{2}

10^{2} +7^{2} =c^{2}

100+49=c^{2}

149=c^{2}

Question 11.

Answer:

a^{2} +b^{2} =c^{2}

12^{2} +9^{2} =c^{2}

144+81=c^{2}

225=c^{2}

15=c

Question 12.

Answer:

a^{2} +b^{2} =c^{2}

5^{2} +1^{2} =c^{2}

25+1=c^{2}

26=c^{2}

### 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.

Answer:

Question 2.

Determine the length of c in the triangle shown.

Answer:

a^{2} +b^{2} =c^{2}

6^{2} +8^{2} =c^{2}

36+64=c^{2}

100=c^{2}

10=c

Question 3.

Determine the length of c in the triangle shown.

Answer:

a^{2} +b^{2} =c^{2}

4^{2} +7^{2} =c^{2}

16+49=c^{2}

65=c^{2}