Shape and Space 3
4 marks · NormalA mobile phone mast is 48 m tall. From a point on level ground, the angle of elevation to the top of the mast is 40°.
Calculate the distance from the point to the base of the mast, correct to 3 significant figures.
Give a reason why the tangent ratio is suitable for this calculation.
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) 57.3 m
(b) Because tangent relates the side opposite (height) and the side adjacent (distance on ground) to the angle in a right triangle.
Common mistakes: Using sine or cosine instead of tangent; Wrong explanation of ratio choice
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets up tan(40°) = 48 / x or equivalent rearranged triangle
A1 (a) · 1 mark · Accurate calculation for x: x = 48 / tan(40°)
A2 (a) · 1 mark · Final answer to 3 significant figures: 57.3 m
B1 (b) · 1 mark · Explains why tangent ratio is suitable: It links opposite and adjacent sides for the given angle.
Worked solution
Let the distance from the point to the base be x:
Rounded to 3 significant figures, x = 57.3 m.
Tangent is used because it relates the height (opposite) to the ground distance (adjacent) for the given angle.