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Tutor profile: Aiden H.

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Aiden H.
Tutor for 2 years
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Questions

Subject: Trigonometry

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Question:

An inquisitive math student is standing 25 feet from the base of the Washington Monument. The angle of elevation from her horizontal line of sight is 87.4∘. If her “eye height” is 5ft, how tall is the monument?

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Aiden H.
Answer:

We can find the height of the monument by using the tangent ratio and then adding the eye height of the student. tan87.4∘h=h25=25⋅tan87.4∘=550.54 Adding 5 ft, the total height of the Washington Monument is 555.54 ft. According to Wikipedia, the actual height of the monument is 555.427 ft.

Subject: Geometry

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Question:

A cube has a surface area of fifty-four square centimeters. What is the volume of the cube?

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Aiden H.
Answer:

The formula for the volume V of a cube with edge-length e is: V = e3 To find the volume, I need the edge-length. Can I use the surface-area information to get what I need? Let's see... A cube has six sides, each of which is a square; and the edges of the cube's faces are the sides of those squares. The formula for the area of a square with side-length e is A = e2. There are six faces so there are six squares, and the cube's total surface area SA must be: SA = 6e2 Plugging in the value they gave me, I get: 54 = 6e2 54 / 6 = (6e2) / 6 9 = e2 3 = e Since the volume is the cube of the edge-length, and since the units on this cube are centimeters, then: the volume is 27 cubic centimeters, or 27 cc, or 27 mL

Subject: Algebra

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Question:

One number is 10 more than another. The sum of twice the smaller plus three times the larger, is 55. What are the two numbers?

Inactive
Aiden H.
Answer:

Let x be the smaller number. Then the larger number is 10 more: x + 10. The problem states: 2x + 3(x + 10) = 55. That implies 2x + 3x + 30 = 55. 5x = 55 − 30 = 25. x = 5. That's the smaller number. The larger number is 10 more: 15.

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