TOA: Error Analysis & Misconceptions

Mathematics
GCSE Foundation
10 questions
~20 mins
1 views0 downloads

About This Worksheet

A worksheet focusing on identifying and correcting misconceptions related to the TOA ratio in trigonometry. Designed for GCSE Foundation students to develop procedural skills and deepen understanding.

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TOA: Error Analysis & Misconceptions

Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet

Grade GCSE Foundation
A

Fluency & Practice

Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the length of side AB in a right-angled triangle where the opposite side to angle C is 5 cm and tan C = 1. Calculate using TOA.
[2 marks]
2.
In a right triangle, side AC (adjacent to angle B) measures 8 cm, and the opposite side is 6 cm. Find angle B using TOA.
[3 marks]
3.
A ladder leaning against a wall forms a 75° angle with the ground. If the ladder is 10 meters long, estimate the height it reaches on the wall.
[2 marks]
B

Problem Solving & Reasoning

Answer all questions. Provide explanations for your reasoning.
1.
A student calculates the tangent of an angle as 0.5 and then finds the hypotenuse in a triangle with an opposite side of 4 cm. Identify the mistake and explain the correct method to find the hypotenuse.
[4 marks]
2.
A right-angled triangle has an angle of 30° and an adjacent side of 10 cm. Using TOA, find the length of the opposite side. Then, evaluate the common misconception that tan 30° is 0.5 without calculator.
[3 marks]
C

Real-world Applications

Solve the problems using your understanding of TOA in real contexts.
1.
A surveyor measures the angle of elevation to the top of a building as 60°. If the surveyor is 50 meters away from the building, estimate the height of the building using TOA.
[3 marks]
D

Challenge & Extension

Attempt these more difficult problems to stretch your understanding.
1.
Construct a right-angled triangle where the tangent of angle θ is 3/4. Use the grid to draw the triangle and label all sides. Then, calculate the hypotenuse.
[4 marks]
2.
Given an error where a student uses sine instead of tangent in a problem involving TOA, identify the mistake and correct the approach.
[3 marks]
E

Mixed Review & Error Analysis

Review the questions carefully. Identify and correct the common mistake shown in each problem.
1.
A student calculates tan 45° as 1.5 and uses it to find a side length. Explain the mistake and provide the correct value for tan 45°.
[3 marks]
2.
A diagram shows a right triangle where students incorrectly assume the tangent of a 60° angle is 1. Identify the misconception and state the correct value.
[3 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet