To sketch the rhombus, we start by drawing a horizontal line of length 10 cm. We then draw a line segment of length 5 cm at an angle of 55 degrees from each end of the horizontal line, going upwards. We then connect the endpoints of these two line segments with a horizontal line of length 10 cm, completing the rhombus.
To show the diagonals, we can draw a line from one corner of the rhombus to the opposite corner. This diagonal will have a length equal to the hypotenuse of a right triangle with legs of 5 cm (half the side length) and 10 cm (the distance between opposite corners). Using the Pythagorean theorem, we can calculate the length of the diagonal:
diagonal^2 = 5^2 + 10^2
diagonal^2 = 25 + 100
diagonal^2 = 125
diagonal = β125 β 11.2 cm
We can repeat this process for the other diagonal:
diagonal^2 = 5^2 + 10^2
diagonal^2 = 25 + 100
diagonal^2 = 125
diagonal = β125 β 11.2 cm
Therefore, the length of both diagonals of the rhombus is approximately 11.2 cm.
To indicate the obtuse angles on the sketch, we can label them using the measure of the angle in degrees. For example, we can label the obtuse angles as 110 degrees, as stated in the problem. If we extend the diagonals to their intersection point, we can also label the angles formed by the diagonals (which are all acute angles).