Adah would like to estimate the height of a tree located at point P on the edge of a riverbank, with the top of the tree at point Q. However, due to a raging river, she is unable to reach the base of the tree. From point M she measures an angle of elevation of 20° to the top of the tree, and then from point N (which is on the edge of Adah’s bank of the river) she measures an angle of elevation of 35° to the top of the tree. Between the points M and N she measures a horizontal distance of 12 m. Points M, N and P all lie on a single horizontal line, and point Q is vertically above point P. The diagram below shows this information.
Calculate the length of NQ.
Calculate the height of the tree.
Adah borrows a boat and crosses the river at a rate of 50 metres per 15 minutes.
Assuming that she crosses in a straight line directly from point N to point P, find out how long it takes her to cross the river.
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