Oliver, a hiker, is trying to work out the height of a tree located between his
campsite and a landmark rock formation. His campsite is located at point A.
The rock formation, where he is standing, is located at point B, 800 metres
in a straight line from his campsite. The tree is located at point C between
the rock formation and his campsite. You can assume that the terrain is flat,
and all three points A, C and B are on a straight line. The top of the tree is
at point D, vertically above point C.
He decides to use a clinometer and his knowledge of trigonometry to work
out the angle of elevation from where he is standing to the top of the tree
(∠ABD). He finds this to be 6
◦
. He then walks back to his campsite and
works out the angle of elevation from the campsite to the top of the tree
(∠BAD). He finds this to be 4
◦
.
(a) Draw a sketch, showing the triangle, ABD. Add point C and join the
points C and D with a dotted straight line. Include the information on
length (in metres) and angles noted above. The sketch does not need to
be to scale. [2]
(b) (i) Calculate the internal angle ∠ADB of the triangle ABD. [2]
(ii) Calculate the distance from the campsite to the top of the tree,
giving your answer correct to the nearest metre. [3]
(iii) Use the result from part (b)(ii) to calculate the height of the tree,
giving your answer correct to the nearest metre.