In trigonometry, a skinny triangle^{[citation needed]} is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to that angle in radians. The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions or tables can be entirely dispensed with.

The skinny triangle finds uses in surveying, astronomy, and shooting.

The approximated solution to the skinny isosceles triangle, referring to figure 1, is:

This is based on the small-angle approximations:

and

when ${\displaystyle \scriptstyle \theta }$ is in radians.

The proof of the skinny triangle solution follows from the small-angle approximation by applying the law of sines. Again referring to figure 1:

The term ${\displaystyle \scriptstyle {\frac {\pi -\theta }{2}}}$ represents the base angle of the triangle because the sum of the internal angles of any triangle (in this case the two base angles plus θ) are equal to π. Since θ is a lot smaller than π, then ${\displaystyle \scriptstyle {\frac {\pi -\theta }{2}}}$ is approximately${\displaystyle \scriptstyle {\frac {\pi }{2}}}$, and sin ${\displaystyle \scriptstyle {\frac {\pi }{2}}}$ = 1. Applying the small angle approximations to the law of sines above results in