The document provides examples of using the Pythagorean theorem (c2 = a2 + b2) to calculate the length of unknown sides of right triangles. It shows applying the theorem to find missing side lengths when given the lengths of two sides, rounding answers to 1 decimal place. It also includes an example of calculating total distance traveled using the theorem.

1. Pythagoras!

2. c =a +b
2 2 2
c
a
b
c must be the hypotenuse - the longest side in a right angle triangle (opposite the
right angle), and a and b are the two shorter sides

3. c2 = a2 + b2
8 cm x2 = 82 + 5.22
x x2 = 64 + 27.04
x2 = 91.04
x = √91.04
x = 9.541488354
5.2 cm x = 9.5 to 1 d.p.

4. x 3 cm x = 5 cm
4 cm
x
5 cm x = 13 cm
12 cm
5 cm
6 cm
x = 7.8 cm (1 dp)
x

5. c2 = a2 + b2
152 = 112 + x2
15 cm 225 = 121 + x2
11 cm
x2 = 225 – 121
x2 = 104
x = √104
x = 10.19803903
x
x = 10.2 to 1 d.p.

6. 11m
xm
x = 6.3 m (1 dp)
9m
23.8 cm
11 cm x = 21.1 cm (1 dp)
x cm
3.4 cm
7.1 cm
x = 7.9 cm (1 dp)
x cm

7. 15 miles
H
B
6.4 miles
L

8. 15 miles
H
B
6.4 miles
L
Total distance travelled = 21.4 + 16.4 = 37.7 miles

9. 12 ft
9.5 ft
L

10. 12 ft
9.5 ft
L
L = 7.3ft

11. Exam Question

12. Exam Question
230

13. Exam Question
13.7