Question

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

a) 13 m
b) 5 m
c) 11 m
d) 18 m

Answer 1

To find the missing side of each triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Therefore, the missing side of each triangle is:

a) 13 m

b) 5 m

c) 13 m

d) 13 m

Explanation:

To find the missing side of each triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

a) For a triangle with one side of length 5 m and the other side of length 12 m, the missing side can be found using the formula:

\[c = \sqrt{a^2 + b^2}\]

\[c = \sqrt{5^2 + 12^2}\]

\[c = \sqrt{25 + 144}\]

\[c = \sqrt{169}\]

\[c = 13\]

b) For a triangle with one side of length 3 m and the other side of length 4 m, the missing side can be found using the formula:

\[c = \sqrt{a^2 + b^2}\]

\[c = \sqrt{3^2 + 4^2}\]

\[c = \sqrt{9 + 16}\]

\[c = \sqrt{25}\]

\[c = 5\]

c) For a triangle with one side of length 5 m and the other side of length 12 m, the missing side can be found using the formula:

\[c = \sqrt{a^2 + b^2}\]

\[c = \sqrt{5^2 + 12^2}\]

\[c = \sqrt{25 + 144}\]

\[c = \sqrt{169}\]

\[c = 13\]

d) For a triangle with one side of length 5 m and the other side of length 12 m, the missing side can be found using the formula:

\[c = \sqrt{a^2 + b^2}\]

\[c = \sqrt{5^2 + 12^2}\]

\[c = \sqrt{25 + 144}\]

\[c = \sqrt{169}\]

\[c = 13\]

Therefore, the missing side of each triangle is:

a) 13 m

b) 5 m

c) 13 m

d) 13 m

Answer 2

a) The missing side lengths of the triangle is: 5 m

b) The missing side lengths of the triangle is: 12 m

c) The missing side lengths of the triangle is: Approximately 16.3 m

d) The missing side lengths of the triangle is: Approximately 22.2 m

Explanation:

To find the missing side of each triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Given the side lengths:

• a) 13 m,12 m, x
• b) 5 m, 13m, x
• c) 11 m, 12m, x
• d) 18 m, 13m, x

Let's find the missing side of each triangle:

a) 13 m,12 m, x

We need to find the missing side, x. Using the Pythagorean theorem, we have:

x² = 13² - 12²

x^2 = 169 - 144

x^2 = 25

x = √25

x = 5 m

b)5 m, 13m, x

We need to find the missing side, x. Using the Pythagorean theorem, we have:

x² = 13² - 5²

x² = 169 - 25

x² = 144

x = √144

x = 12 m

c) 11 m, 12m, x

We need to find the missing side, x. Using the Pythagorean theorem, we have:

x² = 12²+ 11²

x² = 144 + 121

x² = 265

x ≈ √265

x ≈ 16.3 m (rounded to the nearest tenth)

d) 18 m, 13m, x

We need to find the missing side, x. Using the Pythagorean theorem, we have:

x² = 13² + 18²

x² = 169 + 324

x² = 493

x ≈ √493

x ≈ 22.2 m (rounded to the nearest tenth)

Therefore, the missing side lengths of the triangles are:

a) 5 m

b) 12 m

c) Approximately 16.3 m

d) Approximately 22.2 m

Your question is incomplete, but most probably the full question was:

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

a) 13 m,12 m, x

b) 5 m, 13m, x

c) 11 m, 12m, x

d) 18 m, 13m, x