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Vincent A.

Tutor for 7 years. Teach math at private education company.

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Trigonometry

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Question:

A 10 foot ladder is leaned against a wall. The top of the ladder forms a 30 degree angle with the wall. How far is the bottom of the ladder from the base of the wall?

Vincent A.

Answer:

Since the distance of the bottom of the ladder from the base of the wall is opposite the 30 degree angle, we use the sine of 30 to solve this problem because sine is the ratio of the opposite side to the hypotenuse. The ladder itself is the hypotenuse. So the distance from the bottom of the ladder to the base of the wall is 10sin30 = (10)(0.5) = 5 feet.

Geometry

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Question:

A pizza measures 12 inches across its diameter. How many slices are available if each slice has an area of 6pi?

Vincent A.

Answer:

The total area of the pizza is pi*r^2. The radius is 12/2 = 6 inches. So, the area is pi*6^2 = 36pi. Since each slice is 6pi, the number of slices available are 36pi/6pi = 6 slices.

Algebra

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Question:

3 friends want to buy a new video game, but each one does not have enough money. But they decide to buy one game and share it between them. The game costs $63. How much must each friend pay in order to buy the game?

Vincent A.

Answer:

They must divide the cost of the game evenly among themselves. Therefore each must pay 63/3 = 21. So, they must pay $21 each.

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