Prerequisite for Level 4: Completion of Level 3 OR successful completion of assessment interview (for new students).
Given trapezoid ABCD. MN is a mid-line of ABCD. MN = 28cm. Sides AB and CD continued until they meet in point P.
APD = 30°. A circle with diameter MN is drawn with the center O in the middle of mid-line MN. Points B and C are on the circle.
Find length of AD.
Stephanie and Elizabeth live in houses on the same street. The street is straight and there is a very high transmission antenna between their houses. Stephanie observes from her house the top of the antenna at the angle of elevation 33°, but Elizabeth observes from her house the top of the antenna at the angle of elevation 47°. How high is the top of the antenna from the ground, if Elizabeth’s house is 120 meters nearer to the antenna than Stephanie’s house?
Prove the following trigonometric identity:
Prove the following using mathematical induction: 1 + 3 + 5 + 7 + . . . + (2n – 1) = n^2