The Basics
Real-World Contexts
CSEC Exam Style
100
What is the formula for Pythagoras' Theorem, and what type of triangle must it be applied to?
Answer:a2+ b2 = c2 applied exclusively to right-angled (90 degrees
100
A $5 meter ladder leans against a vertical wall, reaching a height of $4 meters. How far is the foot of the ladder from the wall?
What is 3meters
200
How do you identify the hypotenuse in any right-angled triangle?
It is the longest side, located directly opposite the 900 right angle
200
A rectangle has a length of $12 cm and a width of $5cm. Calculate the exact length of its diagonal.
What is 13cm
picture
300
In a right-angled triangle with shorter sides measuring 6cm and 8cm, what is the length of the hypotenuse?
$10cm
300
A person walks 9 km due East, then 12km due North. What is their direct distance (displacement) from the starting point?
What is 15 km
300
A ship sails 14 km East from Point A to Point B, then 20 km North to Point C. Calculate the direct distance AC correct to 2 decimal places.
24.41km = sqrt{142 + 202} = sqrt{196 + 400} = sqrt{596} 24.41.
400
A right-angled triangle has a hypotenuse of $14m and one short side of 6m. Calculate the length of the other side. Give your answer to 2 d.p.
196-36 = square root of 160 12.649 2 dp 12.65m
400
A television screen width is $16\text{ inches}$ and its height is $9\text{ inches}$. Find the diagonal screen size correct to 1 decimal place.
$18.4 inches sqrt{162 + 92} = sqrt{256 + 81} = sqrt{337}= 18.357
500
State whether a triangle with side lengths 7 cm, 24 cm, and 25cm forms a right-angled triangle. Show proof.
Yes. 72 + 242 = 49 + 576 = 625, and 252 = 625. Proof a2 + b2 = c2, it is a right-angled triangle.
500
An isosceles triangle ABC has equal sides AB = AC = 10 cm and base BC = 12 cm. Calculate the perpendicular height of the triangle.
$8 cm (Splitting the base creates two right triangles with base $6cm}=sqrt{102 - 62} = {100 - 36} = sqrt{64} = 8cm.