From the top of a tower of unknown height H metres, the angle of depression of a point P on the horizontal ground is 52∘. A point Q lies on the same horizontal line as P and is 78m closer to the foot of the tower than P. The angle of depression of Q is 70∘.
a. (i) Using a suitable sketch, label all the known and unknown quantities involved.
b. (ii) Write two equations in H and the horizontal distance x (in metres) from the foot of the tower to point Q.
c. (iii) Solve these equations to find H and x. Give each answer correct to the nearest metre.