# Tutor profile: Sophia K.

## Questions

### Subject: Trigonometry

The length of one side of an equilateral triangle is 30 cm. Find the length of an altitude of the triangle.

Since we are working with an equilateral triangle in this question, we know that all three angles have an equal measure of 60 degrees. In addition, since we are asked to find the length of the altitude of the triangle, we need to draw a line that bisects the top 60 degree angle and is perpendicular to the bottom side of the triangle. Now, we are left with two right triangles and the two right triangles both have 30, 60, 90 degree angles. Therefore, we can use the 30:60:90 (1:radical 3:2) right triangle rule to figure out the length of the altitude. Since the 30 degrees angle corresponds to the bottom side (15 cm), we can use the ratio to figure out that the 60 degrees angle corresponds to radical 15radical3.

### Subject: Basic Math

Express 71/1000 as a decimal.

Expressing 71/1000 as a decimal is super easy because we are working with powers of 10! If we express 1000 as a power of 10, we get 10^3 or 10 to the 3rd power. We can also see this easily because 1000 has 3 zeros. Therefore, since we are doing division (71/1000), all we have to do is move three spaces to the left of 71. Thus, 71/1000 is equivalent to 0.071 as a decimal.

### Subject: Algebra

Question: -3x + y =6 Please solve for y.

The first thing you should do when you receive a question is reread it to make sure you fully understand what it is asking you to do. In the following question, we are given an equation and are told to solve for y. When we are asked to solve an equation for a single variable, we need to make sure that we isolate or in other words make the variable be by itself on one side of the equal side. In this case, to isolate the variable y, we need to get rid of the -3x that it is with on the left side of the equal sign. To isolate or get y by itself on the left side of the equal sign we need to take the opposite sign of -3x on both sides. In other words, we need to add 3x on both sides of the equal sign. By doing so, the -3x on the left side of the equal sign cancels out and so we are left with only y on the left side of the equation. Since we added 3x on both sides of the equation, the right side of the equation is therefore 6+3x. Thus, we are left with the following: y=6+3x

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