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AMO 2021 - Secondary 4 (Grade 10) Question 13

AMO · AMO 2021 - Secondary 4 (Grade 10)

Question 13

Terry marks points $A,B$ on the same straight ground line as an oak tree, with $A$ nearer the tree and $AB=6$ yards. In the photograph, the angles of elevation labelled 1 and 2 are $60^\circ$ and $45^\circ$, respectively. Ignoring camera distortion and using the level-ground model shown, what is the tree height in yards?

Question illustration
  1. $6+5\sqrt2$
  2. $15-3\sqrt2$
  3. $12+4\sqrt2$
  4. $9+3\sqrt3$
  5. $8+6\sqrt2$