Non-Right-Angled Triangle

$a^2+b^2=c^2$

Pythagorean Theorem

Enter two known sides. Leave the unknown side blank. The theorem states $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.

Side a:

Side b:

Hypotenuse c:

For an acute angle $\theta$ in a right-angled triangle:

Angle $\theta$ (degrees):

Cosecant ($\csc \theta$): $\frac{1}{\sin \theta} = \frac{\text{Hypotenuse}}{\text{Opposite}}$
Secant ($\sec \theta$): $\frac{1}{\cos \theta} = \frac{\text{Hypotenuse}}{\text{Adjacent}}$
Cotangent ($\cot \theta$): $\frac{1}{\tan \theta} = \frac{\text{Adjacent}}{\text{Opposite}}$

Angle $\theta$ (degrees):

Angle ($\theta$)	$\sin \theta$	$\cos \theta$	$\tan \theta$
$0^\circ (0 \text{ rad})$	$0$	$1$	$0$
$30^\circ (\pi/6 \text{ rad})$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{3}}$ or $\frac{\sqrt{3}}{3}$
$45^\circ (\pi/4 \text{ rad})$	$\frac{1}{\sqrt{2}}$ or $\frac{\sqrt{2}}{2}$	$\frac{1}{\sqrt{2}}$ or $\frac{\sqrt{2}}{2}$	$1$
$60^\circ (\pi/3 \text{ rad})$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}$	$\sqrt{3}$
$90^\circ (\pi/2 \text{ rad})$	$1$	$0$	Undefined

Provide exactly two pieces of information, including at least one positive side length. Angle C is assumed to be $90^\circ$.

Side a (opposite A):

Side b (opposite B):

Hypotenuse c:

Angle A (°):

Angle B (°):

Angle of Elevation: The angle measured upwards from the horizontal line of sight to an object above the observer.

Angle of Depression: The angle measured downwards from the horizontal line of sight to an object below the observer.

Given the height of an object and the angle of elevation to its top from the ground, find the horizontal distance.

Object Height (h):

Angle of Elevation ($\theta$, degrees):

For small angles $\theta$ (measured in radians):

These approximations are useful in physics and engineering for simplifying complex equations under certain conditions.

Enter a small angle (degrees, e.g., ≤ 10°):