Right Triangle Calculator With Angles

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Right Triangle Calculator With Angles

Right Triangle Formulas:

\[ a = hyp \times \sin(\theta) \] \[ b = hyp \times \cos(\theta) \] \[ \theta = \arcsin\left(\frac{a}{hyp}\right) \]

Side a (opposite):

length units

Side b (adjacent):

length units

Hypotenuse:

length units

Angle θ:

degrees

Calculated Results:

Enter any two known values to calculate the others

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1. What is a Right Triangle?

A right triangle is a triangle with one angle equal to 90 degrees. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs (opposite and adjacent).

2. How Does the Calculator Work?

The calculator uses trigonometric relationships in right triangles:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \] \[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \] \[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \]

Where:

\( \theta \) — Angle (in degrees or radians)
opposite — Side opposite to the angle θ
adjacent — Side adjacent to the angle θ
hypotenuse — Longest side opposite the right angle

Explanation: The calculator can determine all unknown sides and angles when any two elements (sides or angle) are known.

3. Right Triangle Formulas

Key Formulas:

Pythagorean theorem: \( a^2 + b^2 = hyp^2 \)
Area: \( \frac{1}{2} \times a \times b \)
Perimeter: \( a + b + hyp \)
Angle relationships: \( \alpha + \beta = 90^\circ \)

4. Using the Calculator

Tips: Enter any two known values (two sides, or one side and one angle). The calculator will compute all missing values. All inputs must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: Any consistent length units can be used (cm, inches, etc.). Angles can be in degrees or radians.

Q2: Can I calculate the area with this calculator?
A: Yes, once all sides are calculated, the area is half the product of the two legs.

Q3: What if I know two angles?
A: In a right triangle, knowing one non-right angle automatically gives you the other (they sum to 90°), but you still need at least one side length to determine sizes.

Q4: How accurate are the results?
A: Results are accurate to 4 decimal places, though practical measurements may limit precision.

Q5: Does this work for non-right triangles?
A: No, different formulas (like the Law of Cosines) are needed for non-right triangles.

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