Hypotenuse Calculator

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Hypotenuse Calculator
Hypotenuse (c) – given legs a and bLeg (a or b) – given hypotenuse and one leg
Result:
Enter values and click Calculate to see results.
function updateLabels(){var mode=document.getElementById('calc_mode').value;if(mode==='hypotenuse'){document.getElementById('label1′).innerHTML='Side a:';document.getElementById('label2′).innerHTML='Side b:';}else{document.getElementById('label1′).innerHTML='Hypotenuse c:';document.getElementById('label2′).innerHTML='Known Leg:';}}function calculateResult(){var mode=document.getElementById('calc_mode').value;var v1=parseFloat(document.getElementById('input1').value);var v2=parseFloat(document.getElementById('input2').value);var showSteps=document.getElementById('steps').checked;var ansDiv=document.getElementById('answer');if(isNaN(v1)||isNaN(v2)){ansDiv.innerHTML='Error: Please enter valid numbers for both fields.';return;}var result=0;var stepsHtml=";if(mode==='hypotenuse'){result=Math.sqrt(Math.pow(v1,2)+Math.pow(v2,2));if(showSteps){stepsHtml='
a\u00B2 + b\u00B2 = c\u00B2
'+v1+'\u00B2 + '+v2+'\u00B2 = c\u00B2
'+(v1*v1).toFixed(2)+' + '+(v2*v2).toFixed(2)+' = c\u00B2
'+(v1*v1+v2*v2).toFixed(2)+' = c\u00B2
c = \u221A'+(v1*v1+v2*v2).toFixed(2)+'
c \u2248 '+result.toFixed(4)+'
';}ansDiv.innerHTML='The length of the Hypotenuse (c) is '+result.toFixed(4)+'.'+stepsHtml;}else{if(v1<=v2){ansDiv.innerHTML='Error: The hypotenuse (c) must be longer than the leg.';return;}result=Math.sqrt(Math.pow(v1,2)-Math.pow(v2,2));if(showSteps){stepsHtml='
a\u00B2 + b\u00B2 = c\u00B2
Leg\u00B2 + '+v2+'\u00B2 = '+v1+'\u00B2
Leg\u00B2 + '+(v2*v2).toFixed(2)+' = '+(v1*v1).toFixed(2)+'
Leg\u00B2 = '+(v1*v1).toFixed(2)+' – '+(v2*v2).toFixed(2)+'
Leg\u00B2 = '+(v1*v1-v2*v2).toFixed(2)+'
Leg = \u221A'+(v1*v1-v2*v2).toFixed(2)+'
Leg \u2248 '+result.toFixed(4)+'
';}ansDiv.innerHTML='The length of the Missing Leg is '+result.toFixed(4)+'.'+stepsHtml;}}

Using the Hypotenuse Calculator

The hypotenuse calculator is a specialized tool designed to solve for the missing side of a right-angled triangle using the Pythagorean theorem. Whether you are a student working on geometry homework or a contractor measuring a roofing pitch, this tool provides instant and accurate results.

To get started, follow these simple steps:

  • Choose Calculation: Select whether you want to find the hypotenuse (c) or one of the legs (a or b).
  • Enter Values: Input the known lengths into the respective boxes.
  • Toggle Steps: Check "Show Pythagorean Theorem Steps" if you need to see the manual calculation process for your records.
  • Calculate: Click the button to see the final result.

How It Works: The Pythagorean Theorem

The fundamental principle behind this hypotenuse calculator is the Pythagorean theorem, which states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Formula: a² + b² = c²

Where:

  • a and b: The "legs" of the triangle (the sides that form the 90-degree angle).
  • c: The "hypotenuse" (the longest side opposite the right angle).

To solve for the hypotenuse specifically, the formula is rearranged as:

c = √(a² + b²)

Practical Calculation Example

Example: Suppose you are building a wooden ramp. The height (leg a) is 3 feet and the horizontal length (leg b) is 4 feet. How long must the ramp board (hypotenuse c) be?

Step-by-step solution:

  1. Identify knowns: a = 3, b = 4
  2. Square the sides: 3² = 9, 4² = 16
  3. Add the squares: 9 + 16 = 25
  4. Take the square root of the sum: √25 = 5
  5. Result: The hypotenuse is 5 feet.

Common Questions

What is the hypotenuse of a triangle?

The hypotenuse is the longest side of a right-angled triangle. It is always located directly opposite the 90-degree (right) angle. In trigonometry, it is the side used as the denominator when calculating sine and cosine ratios.

Can I use this for non-right triangles?

No, the Pythagorean theorem and this hypotenuse calculator only apply to right triangles (triangles with one 90-degree angle). For other triangles (acute or obtuse), you would need to use the Law of Cosines.

Why is it called the Pythagorean Theorem?

It is named after the ancient Greek mathematician Pythagoras, who is traditionally credited with its discovery, although evidence suggests that Babylonian and Indian mathematicians knew of the relationship centuries before him.

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