Question

geometry
pythagorean theorem review
find the missing side of each triangle. round your answers to the nearest tenth if necessary.
1)
6 yd
x
10 yd
2)
4 mi
x
5 mi
3)
12 mi
13 mi
x
4)
15.1 in
x
10.5 in
5)
10 km
5.1 km
x
6)
5.7 cm
9.6 cm
x
state if each triangle is a right triangle.
7)
12 in
9 in
15 in
8)
8 km
6 km
10 km
9)
6 mi
8 mi
12 mi
10)
15 cm
9 cm
10 cm

Explanation:

Step1: Apply Pythagorean theorem to 1

$x^2 + 6^2 = 10^2 \Rightarrow x = \sqrt{100-36} = 8$ yd

Step2: Apply Pythagorean theorem to 2

$x^2 + 4^2 = 5^2 \Rightarrow x = \sqrt{25-16} = 3$ mi

Step3: Apply Pythagorean theorem to 3

$12^2 + x^2 = 13^2 \Rightarrow x = \sqrt{169-144} = 5$ mi

Step4: Apply Pythagorean theorem to 4

$15.1^2 + 10.5^2 = x^2 \Rightarrow x \approx \sqrt{228.01+110.25} \approx 18.4$ in

Step5: Apply Pythagorean theorem to 5

$x^2 + 5.1^2 = 10^2 \Rightarrow x \approx \sqrt{100-26.01} \approx 8.6$ km

Step6: Apply Pythagorean theorem to 6

$5.7^2 + x^2 = 9.6^2 \Rightarrow x \approx \sqrt{92.16-32.49} \approx 7.7$ cm

Step7: Check right triangle for 7

$9^2 + 12^2 = 81+144=225=15^2$ → Yes

Step8: Check right triangle for 8

$6^2 + 8^2 = 36+64=100=10^2$ → Yes

Step9: Check right triangle for 9

$6^2 + 8^2 = 100
eq 12^2=144$ → No

Step10: Check right triangle for 10

$9^2 + 10^2 = 181
eq 15^2=225$ → No

Answer:

1. 8 yd
2. 3 mi
3. 5 mi
4. 18.4 in
5. 8.6 km
6. 7.7 cm
7. Yes
8. Yes
9. No
10. No