Sample Problems on Hypotenuse Formula
Problem 1: Find the hypotenuse of a right angled triangle whose base is 6 cm and whose height is 8 cm?
Solution:
The formula to calculate Hypotenuse:
Hypotenuse =√ (Perpendicular²+ Base²)
c = √(a² + b²)
given ,base (a) =6,and perpendicular (b) =8
hence c = √(36 + 64)
c = √100
c = 10 cm.
Problem 2: Find the base of a right angled triangle whose hypotenuse is 13 cm and whose height is 12 cm?
Solution:
Using the formula to calculate Hypotenuse:
Hypotenuse =√ (Perpendicular²+ Base²)
c = √(a² + b²)
a(perpendicular)= 12, c(hypotenuse) = 13, find b(base)
So b = √(c2 – a2)
hence b = √(169 – 144)
b = √25 = 5 cm
Hence, the base of a right angled triangle =5 cm
Problem 3: Find the perpendicular of a right angled triangle whose hypotenuse is 25 cm and whose base is 7 cm?
Solution:
Using the formula to calculate Hypotenuse:
Hypotenuse =√ (Perpendicular²+ Base²)
c = √(a² + b²)
b(base)= 7, c(hypotenuse) = 25, find a(perpendicular)
so a = √(c2 – b2)
hence a = √(625 – 49)
a = √576
a = 24 cm.
Hypotenuse Formula
Hypotenuse Formula or Hypotenuse Theorem Formula is another name for Pythagoras Theorem. Hypotenuse Formula is used to calculate the third side of the right-angled triangle given the other two sides. Hypotenuse Formula can be defined as a relation among the three sides (hypotenuse, base, perpendicular) of a right-angled triangle. Hypotenuse Formula states that the sum of squares of two small sides(base and perpendicular) is equal to the square of the longest side (hypotenuse).
In this article, we will explore all the basic details of the Hypotenuse Formula, including the mathematical expression, proof, and various solved examples using the Hypotenuse Formula.
Table of Content
- What is the Hypotenuse?
- Hypotenuse Formula in Triangle
- Hypotenuse Formula Proof
- Application of Hypotenuse Formula
- Sample Problems on Hypotenuse Formula
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