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Stanley S.

Math Tutor for Grade School to High School

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Trigonometry

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Question:

In a right triangle ABC with angle A equal to 90 degrees, find angle B and C so that sine(B) = cosine(B)!

Stanley S.

Answer:

Step 1: Given angle A is 90 degrees, there's only one conclusion, angle B and C are not more than 90 degrees and both of them are in the first quadrant. Step 2: If we look at the value of sine and cosine, there is only one angle that has the same value for its sine and cosine. The answer is 45 degrees.

Geometry

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Question:

A triangle has a perimeter of 50 cm. If 2 of its sides are equal and the third side is 5 more than the equal sides, what is the length of the third side?

Stanley S.

Answer:

Given: Perimeter = 50 Let x = Side A Side A = Side B Side B = x Side C = x + 5 Perimeter = the sum of all sides (Side A + Side B + Side C) 50 = x + x + (x + 5) 50 = 3x + 5 45 = 3x 15 = x (Thus , the length of side A is 15 cm) Side C = x + 5 = 15 + 5 = 20 cm

Algebra

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Question:

John was selling tickets for the school festival. He sold 10 more adult tickets than children tickets, and he sold twice as many senior tickets as children tickets. Adult tickets cost $, children tickets cost $2, and senior tickets cost $3. John made $700. How many adult tickets were sold?

Stanley S.

Answer:

Let x = Children tickets Adult tickets = x + 10 Senior tickets = 2x 5(Adult tickets) + 3(Senior tickets) + 2(Children tickets) = 700 5(x + 10) + 3(2x) + 2(x) = 700 5x + 50 + 6x + 2x = 700 13x + 50 = 700 13x = 700 - 50 13x = 650 x = 50 (Thus there were 50 children tickets sold on that day) Adult tickets = x + 10 = 50 + 10 = 60 tickets

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