State if each triangle is a right triangle & use the formula c=a+b ### Example Problem 3Consider a right triangle with the following side lengths:- The length of one leg is 9 yards.- The length of the other leg is 11 yards.- The length of the hypotenuse is $ \sqrt{115} $ yards.### Diagram Description:A right triangle is depicted with the following side labels:- One leg is labeled "9 yd".- The other leg is labeled "11 yd".- The hypotenuse is labeled "$\sqrt{115}$ yd".This type of right triangle can be evaluated further using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.### Mathematical Verification:According to the Pythagorean theorem:\[ c^2 = a^2 + b^2 \]Where:- $ c $ is the length of the hypotenuse,- $ a $ and $ b $ are the lengths of the other two sides.Substituting in the given values:\[ (\sqrt{115})^2 = 9^2 + 11^2 \]\[115 = 81 + 121 \]\[115 = 202 \]Upon simplifying, it appears there might be a mistake in the diagram as $ 81 + 121 = 202 $ does not equal 115. Hence, revisiting the construction or provided values is recommended.### Practical Application:Using these principles can help in fields such as construction, navigation, and various real-life problem-solving situations where measurements and distances need to be calculated accurately.

If a triangle is a right angled, then pythagorus theorem is applicable which is, where H is the…

Answered: State if each triangle is a right…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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State if each triangle is a right triangle & use the formula c=a+b

### Example Problem 3

Consider a right triangle with the following side lengths:

- The length of one leg is 9 yards.
- The length of the other leg is 11 yards.
- The length of the hypotenuse is $ \sqrt{115} $ yards.

### Diagram Description:
A right triangle is depicted with the following side labels:
- One leg is labeled "9 yd".
- The other leg is labeled "11 yd".
- The hypotenuse is labeled "$\sqrt{115}$ yd".

This type of right triangle can be evaluated further using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

### Mathematical Verification:
According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Where:
- $ c $ is the length of the hypotenuse,
- $ a $ and $ b $ are the lengths of the other two sides.

Substituting in the given values:
\[
(\sqrt{115})^2 = 9^2 + 11^2
\]
\[
115 = 81 + 121
\]
\[
115 = 202
\]

Upon simplifying, it appears there might be a mistake in the diagram as $ 81 + 121 = 202 $ does not equal 115. Hence, revisiting the construction or provided values is recommended.

### Practical Application:
Using these principles can help in fields such as construction, navigation, and various real-life problem-solving situations where measurements and distances need to be calculated accurately.

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

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