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Nick F.

Math and Science Tutor with over 2 Decades of Industrial Experience

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Trigonometry

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Question:

The shadow of a vertical tree on flat ground is 20 meters long. The sun is at an angle of 60 degrees above the horizon. How tall is the tree ?

Nick F.

Answer:

Tracing an imaginary line from the top of the tree to the tip of its shadow forms a right triangle with its three sides being the tree, its shadow, and the imaginary line. From trigonometry, we know that the height of the tree equals the length of its shadow multiplied by the tangent of 60 degrees. Height = 20 meters x Tan 60 = 20 x 1.732 Height = 34.64 meters.

Basic Math

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Question:

How do you solve 3 - (-4) ?

Nick F.

Answer:

When subtracting negative numbers, two consecutive negative signs, which is called a "double negative", should be treated as addition. So, 3 - (-4) should be treated as 3 + 4, which equals 7.

Algebra

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Question:

Expand this expression by multiplying: (y + 3)(y + 4)

Nick F.

Answer:

This requires four multiplication steps, and adding the four products as follows: The leftmost terms in each of the two parenthesis, in this case the y terms, are First. Multiplying them gives y^2, which is y squared. The Outer terms are y and 4. Multiplying them gives 4y. The Inner terms are 3 and y. Multiplying them gives 3y. The rightmost terms in each of the two parenthesis, the 3 and 4, are Last. Multiplying them gives 12. To remember the steps to obtain the four products, note that the first letters of the words First, Outer, Inner, and Last can be used to spell FOIL. Now we add up the four products we obtained above. The result is y^2 + 4y + 3y + 12. Combining the simple y terms gives the simplest form of the result, y^2 + 7y + 12

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