Determine the area of a 30-60-90 triangle with a hypotenuse that is 12 feet long.
All 30-60-90 triangles are proportional to one another. The side across from the 60 degree angle is always the length of the side across from the 30 degree angle multiplied by the square root of 3. And The hypotenuse is always double the length of the side across from the 30 degree angle. (Geometry is usually way more effective to explain with pictures and graphics). To determine the area of this triangle, we need to determine the size of its base and its height. Because its a 30-60-90 triangle, if the hypotenuse is 12, then the side across from the 30 degree angle will be 6 and the side across from the 60 degree angle will be 6*sqrt(3). (Again, that can be explained much better with pictures). The formula for the area of a triangle is 1/2 * base * height. So, the area = 1/2 * 6 * 6sqrt(3), which equals: 18sqrt(3).
Solve the Following Equation for the value of x: 3x + 10 = 25
We would first subtract 10 from each side of the equation because subtraction is the opposite of addition and what we do to one side, we must do to the other. That would give us 3x = 15 Then we would divide each side of the equation by 3 because division is the opposite of multiplication and what we do to one side, we must do to the other. That would give us the solution to the problem x = 5.
Determine if the following lines are parallel, perpendicular, or neither: 10x + 5y = 20 4x + 10y = 24
Well first of all, we must note that: Parallel lines have equal slopes and In perpendicular lines, the slopes are the negative reciprocal to one another. The easiest way to determine the slopes of each line is to put each of the equations in slope intercept form. We do that by solving each equation for Y. For the first equation: We subtract both sides by 10x in order to get the 5y on the side all by itself. That leaves us with: 5y = -10x + 20. Now we must divide both sides of the equation by 5 in order to the Y by itself. That leaves us with: y = -2x + 4. The slope of this equation is -2. For the 2nd equation: We subtract both sides by 4x in order to get the 10y on the side all by itself. That leaves us with 10y = -4x + 24. Now we must divide both sides of the equation by 10 in order to the Y by itself. That leaves us with y = -0.4x + 2.4. The slope of this equation is -0.4 or -2/5. Since -2 and -0.4 are not the same the lines are not parallel. Since -2 and -0.4 are not negative reciprocals to one another, the lines are not perpendicular. Since the equations are different from one another, the lines are not the same line. Therefore, the answer is Neither. The lines are just regular intersecting lines.