Tutor profile: Emma W.

A 25 foot tall flagpole casts a 42 foot shadow. What is the angle that the sun hits the flagpole?

I would begin by drawing a right triangle. We know the height (25ft) and length (42 ft), but we are missing the hypotenuse. The angle we are trying to find is the angle opposite of the length. Since we know the angles opposite and adjacent side lengths we can use Tangent (which is equal to the opposite side divided by the adjacent side) to create an equation to solve for X. This would create TanX= 42/25, solve for X and you get x to be 42/25 times 1/Tan.

9 / (1/2) = **nine divided by one half

You can think of this as a model or by thinking of the algorithm. If you were to create a model I would draw 9 circles and you are trying to find how many groups of 1/2 you can get out of 9 circles. So you would split each of the 9 circles in half, and you are left with 18 halves, so 9 divided by one half is 18. If you think of it as the algorithm, then when you divide by a fraction you are actually multiplying by the reciprocal. So nine divided by 1/2 becomes nine times 2 which is 18.

Solve for X: 5x+9=24

In order to solve for X, you need to isolate the variable. In order to accomplish this you have to subtract 9 on both sides of the equal sign. This is necessary to do to both sides because you have to balance your equation. You are subtracting because you are doing the opposite of adding 9 in the original equation. You are now left with 5x=15. In order to get X isolated, we must do the opposite of multiplication, so we must divide by 5 on both sides of the equals sign. You will be left with the answer of X=3. I suggest checking you answer by putting 3 back into the original equation and to make sure that the equation is still true.