Imagine you have a kite that has a string that's 400ft long. If the string makes an angle of 62 degrees with the ground, what's the height of the kite from the ground to the nearest foot?
Here, we'll use the SOHCAHTOA rule. Since I'm using a regular keyboard, I'll use x to represent theta. Friendly reminder, SOH is Sin x=opposite/hypotenuse; CAH is cos x= adjacent/hypotenuse; TOA is tan x=opposite/adjacent. Alright now draw a right triangle with the right angle on the bottom left corner. Label the hypotenuse at 400 because the represents the length of the string (of the kite). Label the bottom right angle 32 degrees and label the line of the triangle that's directly across from is y. | \ y| \400 |__32 \ Your triangle should roughly look like the one I've tried to construct above. Since the the variable y is opposite the 32 degree angle, and we have the hypotenuse, we'll be using SOH. The equation is is sin 32=y/400. Multiply both sides by 400 to get 400 sin 32=y. Type that in a calculator and you get about 221 ft as your answer.
First, I'll start by explaining the reasoning behind the parenthesis. No, they're not necessary. I only have them there to show there there is, in fact, a negative sign before the 14. Moving on. The first thing you'll do is subtract 21 on both sides. You can't subtract the 21 from the 5x because there is variable behind the x, therefore making the 5 "untouchable" in this case. Your new equations should read 5x=(-35) Now we'll divide both sides by 5. We do this to separate the 5 from the x. I know earlier I said 5 was untouchable. This is an exception because by dividing, we're getting rid of the 5 completely to get the x by itself. -35/5=(-7.) Therefore x=(-7)
Because of the distributive property of multiplication, and PEMDAS, we'll start by multiplying 3 by 2x. That gives us 6x. Next, we'll multiply 3 by 9 to give us 27. So right now our new expression reads 6x+27. Continuing on, well multiply -9 by 4y. We're using a negative 9 instead of a positive one because of the minus sign in the middle of the problem. -9 multiplied by 4y is -36y. So we have 6x+27-36y. Finally, we multiply -9 by -6 to get positive 54 because two negatives multiplied by each other is a positive. So our expression is 6x+27-36y+54. Since we have two numbers without a variable, 27 and 54, we can add them to get 81. So our simplified expression is 6x-39y+81