**For this exercise we will determine the the RADIUS of an arc if we know the RISE and the CHORD.**

In this exercise we will take a **36 inch long ruler** (Line **“B – “C”**) and place it across the arc. The ruler must be straight and both ends of the ruler must be touching the arc. Any length ruler or straight edge will do, just as long as you know its length and where its **midpoint** is.

Now measure the vertical height (Line **“A” – “D”**) at the **halfway point** of line **“B – “C” (Point “D”)** which is at the **18 inch mark** of the ruler. The height in this case will be** 1.25 inches**.

On your calculator punch in **1.25 ÷** by** 18** = you get **.06944**. Now hit **INV** or on some calculators **2nd**. Now punch in **TAN x 2 =** You get **7.945**

Now hit **SIN** then the key **1/x** You should have **7.2347** Now **x 18 =** You get **130.225**.

The **RADIUS** of this arc is** 130.23 inches**.

**In short:**

**Rise ÷ (1/2 of chord) =____ INV or 2nd TAN x 2 = ____ SIN 1/X x (1/2 of chord) = RADIUS**

*This exercise is good for all arcs of less than 180 degrees of arc.
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