Two-Point Anchor Angles: The Simple Trig Behind the Rules

By Grant Prattley
September 29, 2026

Two-Point Anchor Angles:

The Simple Trig Behind The Rules

Most rope courses teach an anchor angle rule. The usual version says stay under 90 degrees for two-point marginal anchors. My recommendation is tighter: keep two-point anchor angles at 60 degrees, with 45 to 60 as the sweet spot. I’ve explained why in another post. Check this out at the end.

Whichever number you use, sooner or later a student asks where it comes from, and “that’s the rule” doesn’t hold up for long.

This article works through the maths for a basic two-point symmetrical anchor. There are several ways to do it. This is the one I’ve found most direct and easiest to follow.

Three ideas to start

Equal angles, equal loading. On a symmetrical anchor, both legs sit at the same angle from the line of the load, so both carry the same tension.
Solve one side only. Because the legs have equal tension, you only need to work out one of them. Use 50% of the load and 50% of the anchor angle.
Use trigonometry. A right triangle drawn on one side of the anchor gives you everything you need to find the tension in that leg.

SOH CAH TOA

Trigonometry is the maths of triangles. In any right-angled triangle (one with a 90-degree corner), the angles and the lengths of the sides are directly linked. Change an angle and the sides change with it, always in the same proportion.

Trig functions are shortcuts for those proportions. Enter an angle, and a trig function tells you how long one side is compared with another. There are three: sine (SIN), cosine (COS) and tangent (TAN). Each compares a different pair of sides, and SOH CAH TOA is the memory aid for which pair goes with which:

The hypotenuse is always the longest side, opposite the right angle.

The adjacent side runs from the angle you’re working with to the right angle. Two sides touch your angle, and the adjacent is the one that isn’t the hypotenuse.

The opposite side sits directly across from the angle you’re working with. It’s the only side that doesn’t touch that angle.

You don’t need to work any of this out by hand. The calculator on your phone will do it. Turn on the scientific mode, and keys appear, including SIN, COS and TAN. Enter the angle and press COS. Make sure it’s in degrees, not radians.

Setting up the triangle

The load (the mg force – mg stands for mass gravity) acts on the focal (master) point. For every action, there is an equal and opposite reaction, so there is an equal force in the opposite direction (the reaction or Normal force). The anchor legs together hold this force, with each taking an even share. The anchor angle determines how much each leg carries beyond 0.50 (50%).

HYP, the hypotenuse, is the leg tension we’re solving for.
ADJ, the adjacent side, is the vertical vector, carrying half the load.
θ/2 is half the anchor angle θ, measured between the anchor leg and the vertical Fₙ.

Note: When a straight line crosses two parallel lines (transversal), it creates pairs of alternate angles. These sit on opposite sides of the crossing line, both between the two parallels, and they are always equal. The red triangles in the diagram mark a pair of alternate angles.

Solving the equation

We know the adjacent side (half the load) and the angle (half the anchor angle), and we want to know the hypotenuse. Adjacent and hypotenuse mean CAH.

\cos θ = \frac{ADJ}{HYP}

The hypotenuse represents the tension in the anchor leg, which is the number we’re after. It sits on the bottom of the fraction, so we need to rearrange the equation to get it on its own.

Multiply both sides by HYP to get it off the bottom:

HYP \cdot \cos θ = \frac{ADJ \cdot HYP}{HYP}

Then divide both sides by cos θ to get HYP on its own:

\frac{HYP \cdot \cos θ}{\cos θ} = \frac{ADJ}{\cos θ}

Which leaves:

HYP = \frac{ADJ}{\cos θ}

Plugging in the numbers

All examples below use a load of 1. That means ADJ = 1/2 = 0.5. Just plug in 0.5 for ADJ in each equation.

Anchor Angle Calculations

Anchor angle: 15°

Half the angle: $\frac{15 °}{2} = 7.5 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (7.5 °)}

HYP = \frac{0.5}{0.991}

HYP = 0.50

Each anchor leg carries about 0.5 (50%) of the load.

Anchor angle: 30°

Half the angle: $\frac{30 °}{2} = 15 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (15 °)}

HYP = \frac{0.5}{0.966}

HYP = 0.52

Each anchor leg carries about 0.52 (52%) of the load.

Anchor angle: 45°

Half the angle: $\frac{45 °}{2} = 22.5 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (22.5 °)}

HYP = \frac{0.5}{0.924}

HYP = 0.54

Each anchor leg carries about 0.54 (54%) of the load.

Anchor angle: 60°

Half the angle: $\frac{60 °}{2} = 30 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (30 °)}

HYP = \frac{0.5}{0.866}

HYP = 0.58

Each anchor leg carries about 0.58 (58%) of the load.

Anchor angle: 75°

Half the angle: $\frac{75 °}{2} = 37.5 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (37.5 °)}

HYP = \frac{0.5}{0.793}

HYP = 0.63

Each anchor leg carries about 0.63 (63%) of the load.

Anchor angle: 90°

Half the angle: $\frac{90 °}{2} = 45 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (45 °)}

HYP = \frac{0.5}{0.707}

HYP = 0.71

Each anchor leg carries about 0.71 (71%) of the load.

Anchor angle: 120°

Half the angle: $\frac{120 °}{2} = 60 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (60 °)}

HYP = \frac{0.5}{0.5}

HYP = 1.00

Each anchor leg carries exactly 1.00 (100%) of the load.

Anchor angle: 150°

Half the angle: $\frac{150 °}{2} = 75 °$

Find the hypotenuse:

HYP = \frac{ADJ}{\cos θ}

HYP = \frac{0.5}{\cos (75 °)}

HYP = \frac{0.5}{0.259}

HYP = 1.93

Each anchor leg carries about 1.93 (193%) of the load.

Quick reference table

Summary

To work out the load on each leg of a symmetrical two-point anchor, draw a right triangle on one leg. Half the load is the adjacent side, the leg tension is the hypotenuse, and the angle is half the anchor angle.

CAH Swap

CAH gives you $\cos θ = \frac{ADJ}{HYP}$ , and rearranged gets you $HYP = \frac{ADJ}{\cos θ}$ .

The anchor angle decides how far each leg climbs above 0.50 (50%). At 60 degrees, it’s 0.58, at 90 it’s 0.71, and at 120, each leg holds 1.00, the full load.

Keep two-point marginal anchor angles at 60 degrees, with 45 to 60 as the sweet spot. I’ve explained why in another post: Two-Point Anchor Angles. The Case For Building In Error

Grant Prattley

Instructor Rescuer Guide Author Consultant

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Two-Point Anchor Angles: The Simple Trig Behind the Rules