Pythagorean Theorem and Example Questions

The Pythagorean Theorem states that in any right triangle, the sum of the squares of the two legs equals the square of the hypotenuse:
where [a] and [b] are the lengths of the legs (sides adjacent to the right angle), and [c] is the length of the hypotenuse (side opposite the right angle).

Example Questions with Solutions

Example 1: Finding the Hypotenuse
Problem: A right triangle has legs of 3 units and 4 units. Find the hypotenuse.
Solution:
Answer: The hypotenuse is 5 units.

Example 2: Finding a Missing Leg
Problem: The legs of a right triangle are 5 and 12. What is the hypotenuse ?
Solution:
Answer: The hypotenuse is 13.

Example 3: Finding a Leg (Not Hypotenuse)
Problem: One leg is 8 and the hypotenuse is 17. Find the other leg.
Solution:
Answer: The missing leg is 15.

Example 4: Real-World Application
Problem: Kelvin is building a gazebo and wants to place a 10-inch wooden bracket diagonally in a corner, with equal distances from the corner to each end. How far below the corner should he fasten it? (Round to nearest tenth)

Solution: Let [x] be the distance from the corner. Since distances are equal:
Answer: Fasten the bracket approximately 7.1 inches below the corner.


















Komentar

Posting Komentar

Postingan populer dari blog ini

Understanding About Menthol

Gambar
Menthol is a natural organic compound derived mainly from peppermint oil and other mint plants, characteristic cooling sensation on the skin and mucous membranes. It can be obtained by extracting mint oils or produced synthetically in the laboratory. What is menthol Menthol is a clear, colorless crystalline substance with a strong, minty smell and taste. It can exist in different stereoisomers, the most common natural form being (–)-menthol (l‑menthol), while the synthetic version is often a racemic mixture (±)-menthol. How it works in the body Menthol creates a cooling sensation because it activates cold receptors on the skin and mucous membranes, primarily the TRPM8 ion channels (and partly TRPA1), which send “cold” signals to sensory nerves. This stimulation produces a soothing, mildly local‑anesthetic effect and can help relieve mild itching, pain, and airway irritation. Main uses Skin and muscle care: Used in creams, balms, or gels for muscle pain, soreness, and mild h...
Baca selengkapnya

Inedible Crabs And Why

Gambar
Some crabs are inedible because they are either poisonous, contain strong toxins, have very little meat, or are unsafe to eat for health reasons.  Why some crabs are not edible Toxic or poisonous species Certain crabs, especially in the family Xanthidae (like some “mud crabs”), naturally accumulate toxins that can be deadly to humans, even when cooked.  In some regions, small reef crabs (for example Zozymus aeneus) are considered venomous and are avoided as food.  Toxin‑loaded organs (even in edible species) In otherwise eatable crabs (like Dungeness or blue crabs), health authorities warn against eating the viscera (“butter” or guts) because it can accumulate domoic acid or other toxins that cause serious illness.  These toxins come from polluted water or harmful algal blooms, so the same crab species may be safe in one area but dangerous in another.  More shell than meat Some crabs (such as stone crabs or certain king‑crab variants) have claws or b...
Baca selengkapnya

Various Superfoods The Rich Nutrients

Gambar
Superfoods are foods that are rich in nutrients such as vitamins, minerals, fiber, antioxidants, and healthy fats. They are not magic foods, but they can be a very healthy part of a balanced diet. Examples of superfoods Blueberries. Salmon. Avocado. Spinach. Broccoli. Chia seeds. Nuts. Eggs. Yogurt or kefir. Sweet potatoes. Simple explanation Blueberries are famous because they contain antioxidants and vitamins. Salmon is a superfood because it gives protein and omega-3 fats. Avocados are rich in healthy fats, fiber, and potassium. Leafy greens like spinach and kale are also considered superfoods because they are full of vitamins and minerals.
Baca selengkapnya