Tina L.

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Trigonometry

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Question:

If one of the angles of a right triangle is 45 degrees, how many degrees are the other two angles of the triangle?

Tina L.

Answer:

The 3 angles of a triangle always sum up to 180 degrees. That gives us a relationship that we can use to find the answer to the question. Let's represent that relationship in mathematical form. I'll have A, B, and C represent those 3 angles, and then the relationship in mathematical form is A + B + C = 180 degrees. The problem statement tells us that one of those angles is 45 degrees. Let's say that's angle A. And the statement also says that the triangle is a right triangle. All right triangles have one angle that is 90 degrees; let's make that angle B. With those 2 pieces of information let's put them into the equation we have. It then becomes 45 + 90 + C = 180. Here we have only 1 variable (angle C) and the other terms are all numbers so we can solve for the angle C. 135 + C = 180 C = 180 - 135 C = 45. Shortcut: Some people memorize the fact that a right triangle with 45 degrees is an isosceles triangle. This means the triangle always has two equal angles and two equal sides.

Pre-Algebra

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Question:

What is the difference between natural numbers and integers?

Tina L.

Answer:

Natural numbers and integers are categories of numbers that have similar properties, but there is a major difference between them. Examples of natural numbers are 0, 1, 2, 3, 4, 5, etc. Examples of integers are 0, -1, 1, -2, 2, -3, 3, -4, 4, -5, 5, etc. Natural numbers are called "natural" because we use them in everyday life for counting. It's numbers that we naturally use. I like to think of apples at the grocery store; you can buy 1 apple, but you can't buy a -1 apple. Integer numbers are numbers that are whole. They can be expressed without decimals or fractions. That's why BOTH negative and positive whole numbers can fall into the "Integer" category. Another way to think about the word, "Integer" is that if a person has "integrity", it means that person is honest and staying true to their whole self. A person of integrity doesn't compromise any of their values. Natural numbers fall into the Integer category, because they're also whole numbers. In contrast, not all Integers --- the negative ones--- are "natural".

Basic Math

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Question:

What is the difference between a nominal number and a cardinal number?

Tina L.

Answer:

Nominal describes numbers that are used like labels to represent something. Nominal numbers usually serve identification purposes, especially when you have many items to label. For example, in a zombie TV show or a story about a disease breakout, someone might say “patient zero”. There are a lot of people who’ve been infected with the disease, but the number “zero” identifies that patient as the FIRST one to catch that disease. Zip codes are a great example of nominal numbers. Because there are so many areas out there, instead of naming every area of land with English words, like “Springfield”, we use nominal numbers. In fact, there are many Springfield cities in the United States, but there’s only 1 area with the zip code 05156. This last example is used in sports competitions like the Olympics. 1st, 2nd, and 3rd place are using a nominal numbers to indicate how well an athlete did in comparison to other athletes. Nominal numbers are useful for communication, when there are a lot of simliar things and you want to differentiate them from each other.

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