Right Triangle Calculator
What is a Right Triangle?
A right triangle is a triangle with one 90-degree (right) angle. The two sides that form this right angle are called the legs, and the longest side opposite the right angle is called the hypotenuse. Right triangles are fundamental in geometry and are widely used in trigonometry, physics, engineering, and construction.
Formulas Used in the Right Triangle Calculator
This calculator is designed to solve right triangles using three different scenarios:
1️⃣ Given Two Sides → Find the missing side and angles using the Pythagorean Theorem & trigonometry.
2️⃣ Given One Angle & One Side → Find the two missing sides and remaining angle using trigonometric functions.
3️⃣ Given Area & One Side → Find the other side and angles using the area formula and trigonometry.
Right Triangle Calculation Methods
1. Finding the Missing Side (Using Pythagorean Theorem)
The Pythagorean Theorem states:
a2 + b2 = c2
where:
- a and b are the legs
- c is the hypotenuse
Example Calculation:
If Side A = 3 and Side B = 4, then:
32 + 42 = c2
9 + 16 = 25
c = √25 = 5
So, the hypotenuse = 5.
2. Finding Missing Angles (Using Trigonometry)
The trigonometric functions used for right triangles are:
sin(θ) = opposite/hypotenuse
cos(θ) = adjacent/hypotenuse
tan(θ) = opposite/adjacent
If we have two sides, we can use inverse trigonometric functions to find angles:
θ = sin−1(opposite/hypotenuse)
Example Calculation:
If Side A = 3 and Side C (Hypotenuse) = 5, then:
θ = sin−1(3/5)
θ = sin−1(0.6) ≈ 36.87°
The other angle is:
90° − 36.87° = 53.13°
3. Finding Sides Using an Angle and One Side
If an angle and one side are given, we use trigonometry:
- Given Angle and Hypotenuse:
- Opposite Side = Hypotenuse × sin(Angle)
- Adjacent Side = Hypotenuse × cos(Angle)
- Given Angle and One Leg:
- If you have the opposite side, find the adjacent side using tan(Angle)
- If you have the adjacent side, find the opposite side using tan⁻¹(Angle)
Example Calculation:
If Angle A = 30° and Side A = 5, then:
Side B = 5 × tan(30°) = 5 × 0.577 = 2.89
Hypotenuse = 5/sin(30°) = 5/0.5 =10
4. Finding Missing Side from Area
The area formula for a right triangle is:
Area = 1/2 × Base × Height
If the Area and one side are known, we rearrange the formula to solve for the missing side:
Height = (2×Area)/Base
Example Calculation:
If Area = 24 and Base = 6, then:
Height = (2×24)/6 = 48/6 = 8
Now, use the Pythagorean theorem to find the hypotenuse.
Conclusion
Understanding right triangle calculations is essential for construction, design, physics, and geometry. Whether you’re solving for missing sides, angles, or area, this Right Triangle Calculator makes it simple!
FAQs (Frequently Asked Questions)
How do you find a missing side in a right triangle?
Use the Pythagorean theorem: a2 + b2 = c2
or trigonometric functions (sin, cos, tan) if you have an angle and one side.
What is the hypotenuse?
The hypotenuse is the longest side in a right triangle, opposite the 90-degree angle.