Question

geometry
mod, 13.3 quiz
name
find the missing side of each triangle. round your answers to the nearest tenth if necessary.
1)
2)
3)
4)
5)
6)
state if the three sides lengths form a right triangle.

1. 9, 12, 15

a) no b) yes

1. 9, 12, 19

a) no b) yes

Explanation:

Problem 1: Find the missing side (Right Triangle, Hypotenuse 13, Leg 5)

Step1: Identify the formula (Pythagorean theorem: \( a^2 + b^2 = c^2 \), where \( c \) is hypotenuse, \( a, b \) are legs)

Let \( c = 13 \), \( b = 5 \), find \( a = x \). So \( x^2 + 5^2 = 13^2 \)

Step2: Solve for \( x^2 \)

\( x^2 = 13^2 - 5^2 = 169 - 25 = 144 \)

Step3: Find \( x \)

\( x = \sqrt{144} = 12 \)

Step1: Apply Pythagorean theorem: \( a^2 + b^2 = c^2 \), \( a = 12 \), \( b = 9 \), \( c = x \)

\( x^2 = 12^2 + 9^2 \)

Step2: Calculate \( x^2 \)

\( x^2 = 144 + 81 = 225 \)

Step3: Find \( x \)

\( x = \sqrt{225} = 15 \)

Step1: Use Pythagorean theorem: \( 6^2 + x^2 = 10^2 \)

Step2: Solve for \( x^2 \)

\( x^2 = 10^2 - 6^2 = 100 - 36 = 64 \)

Step3: Find \( x \)

\( x = \sqrt{64} = 8 \)

Answer:

12

Problem 2: Find the missing side (Legs 12 and 9, Hypotenuse \( x \))