Shape and Space 3
4 marks · NormalA man is standing on a riverbank. Across the river is a tree. The width of the river is 18 m. The angle of elevation from the man’s feet to the top of the tree is 25°. The tree is vertical and the ground is level.
Calculate the height of the tree. Give your answer correct to 1 decimal place.
Explain why the triangle used in your calculation is a right-angled triangle.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 8.4 m
(b) The triangle formed is right-angled because the height of the tree is vertical and the ground is horizontal (so the line from the man to the base and the height of the tree are perpendicular).
Common mistakes: Mixing up base and height; Not providing explanation
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets up triangle with height = 18 × tan(25°)
A1 (a) · 1 mark · Carries out calculation using appropriate trigonometric ratio
A2 (a) · 1 mark · Gives answer correct to 1 decimal place: 8.4 m
B1 (b) · 1 mark · Explanation: right angle formed as tree is vertical, ground is horizontal
Worked solution
Rounded, height = 8.4 m.
The triangle is right-angled because the tree is vertical and the ground is level, so the diagram forms a right triangle.