# Tutor profile: Elizabeth J.

## Questions

### Subject: Trigonometry

If you are given a 45-45-90 triangle with a side length of 4, how long is the hypotenuse?

We will use sin(x) for this example. Referring back to SohCahToa (sine=opposite/hypotenuse, cosine=adjacent/hypotenuse, tangent=opposite/adjacent), we will use sin=opposite/hypotenuse to find the hypotenuse. sin(45) = opp/hyp sin(45) = 4/hyp (then solve to get h by itself) sin(45) x hyp = 4 (multiply by hypotenuse on both sides) hyp = 4/sin(45) (divide by sin(45)) Solve. Hypotenuse = 5.66

### Subject: Geometry

If you are given a triangle with a right angle and lengths of the sides 3 and 4, what is the hypotenuse of the triangle?

To find the hypotenuse of a triangle, refer to the Pythagorean Theorem (a^2 + b^2 = c^2). Since we know the two lengths of the sides of the triangle (3 and 4) we can plug those in for 'a' and 'b'. 3^2 + 4^2 = c^2 9 + 16 = c^2 25 = c^2 Now take the square root of both sides to get c=5.

### Subject: Algebra

Sally goes to the grocery store to buy some fruit. She wants to buy 2 oranges and some apples. An orange costs $1.50 and an apple costs $1.75. If she goes to the store with $10, how many apples can she buy?

If you write out an equation, it would look like this: 10 = 1.75a + 1.50b with a=the number of apples, and b=the number of oranges. If you plug in the 2 oranges in the equation, it looks like: 10 = 1.75a + 3.00 If Sally has $10, subtracting the cost for the oranges, she has $7.00 left: 7 = 1.75a Solve for a to find the number of apples Sally can buy. (7/1.75 = 4) Sally can buy 4 apples.

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