Phillip C.

Stanford Student, Tutor for 5 Years

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Trigonometry

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Question:

Given a right triangle with hypotenuse of length 12 and interior angel A = 60 degrees, what is the X length of the side opposite of the interior angle A?

Phillip C.

Answer:

Given that it is a right triangle with a hypotenuse given and an 'opposite' side in question, we will be looking to use the sine function. Knowing that sine(angle) = opposite/hypotenuse, we derive this formula: sine(60) = x/12 Now, knowing that sine(60) = sqrt(3)/2, we simply multiply both sides of the equation by 12 to get that the side is of length 6sqrt(3).

Geometry

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Question:

What is the measure of an individual interior angle of a regular decagon?

Phillip C.

Answer:

Using the equation for interior angles of regular polygons: [(n-2)*180]/n -- Where n is the number of sides. We simply substitute in 10 for n, and find that an individual interior angle of a regular decagon equals 144 degrees.

Algebra

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Question:

John and Sally are each given $10 by their parents to purchase apples from a store. Since John and Sally have different tastes in apples, they each spend their $10 on a different kind of apple. John decides on a Red Delicious apple and was able to buy 12 apples. Sally chose to purchase Fuji apples and was able to buy 15 apples. Assuming John and Sally both spent all of their money, how much more expensive is a Red Delicious apple than a Fuji apple at this store?

Phillip C.

Answer:

There is a lot on unnecessary words, making this question look like a tricky word problem. In reality, we only have 2, fairly simple equations, one for each kid. John: 12(x) = 10.00 Where x is the price of an individual Red Delicious apple (in dollars). 1. Dividing both sides of the equation by 12, we get x = $0.83 Sally: 15(y) = 10.00 Where y is the price of an individual Fuji apple (in dollars). 1. Dividing both sides of the equation by 15, we get y = $0.67 Now, we do x-y to find how much more expensive an individual Red Delicious apple is than a Fuji apple. 1. 0.83 - 0.67 = $0.16 <- Final answer: A Red Delicious apple is 16 cents more expensive than a Fuji apple.

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