sinx = 1/2. Write 3 possible values of x.
Using a calculator, arcsin 1/2 = 30, so x= 30 Using the symmetry of sine curve, there is another value between 0 and 180. 180 - 30 = 150, so x=150. Finally, as the sine curve has a period of 360, this means we can add 360 to any of our previous solutions for another one. 30 + 360 = 390. so x=390
The angles of a quadrilateral taken in order are x, 5x, 2x and 4x. Which of the following is the quadrilateral: a) kite b) parallelogram c) rhombus d) arrowhead e) trapezium
We can deduce from the question that all the angles are different in this quadrilateral. So we can rule a) b) and c) then. A Kite has 1 pair of equal angles, and a rhombus and parallelogram have 2 pairs of equal angles. As the sum of the interior angles of quadrilateral are 360 degrees, we can set up the equation: x + 5x + 2x + 4x = 360 12x = 360 x = 30 If x = 30, then the largest angle 5x is 150. As an arrowhead must have an angle greater than 180 degrees, the answer but be e) trapezium
The ratio of John's age to Bill's age is 1:2. In 12 years, the ratio of their ages will be 3:5. Calculate their ages.
J:B in 12 years: x:2x x+12:2x+12 = 3:5 (x+12)/3 = (2x+12)/5 5(x+12) = 3(2x+12) 5x+60 = 6x+36 x = 24 John is 24, Bill is 48