**The Story of Sohcahtoa**

After hours of studying geometry, a young Native American boy asked his father who was chief of the Algebra tribe, "Why do they call me, Sohcahtoa?"

His father replied, "Your name is a discovery of your life. Only you can unlock its meaning.

**Any sign of the Sine?**

**Tanned pelts and trickling teepees**

**His boyhood**

While fishing at the river junction, Sohcahtoa stumbled across the mighty Sine tribe, who were longtime enemies of the Algebra tribe. He was fortunate as they had forgotten their weapons at their camp.

If Sohcahtoa could get to his camp before nightfall, he knew that his tribe could prepare themselves for a Sine invasion.

Sohcahtoa knew that his Algebra tribe's camp was a 4 hour trip directly south of the enemy Sine camp.

The Sine immedately went to their camp to retrieve their weapons.

Remembering what he just learned, Sohcahtoa knew that the opposite side of a right triangle had a special relationship to the hypotenuse. He called this relationship "Sine" after the enemy.

Obviously, Sohcahtoa, was unhappy with his father's answer. In frustration, he went back to his geometry book.

Sohcahtoa went on, "My brother is named "Moonhawk" due to his outstanding night vision. My sister is called "Tenderheart" because of her compassion. "

Several uneventful months had passed and Sohcahtoa felt no closer to uncovering the meaning of his name. He had however discovered a neat relationship between the opposite and hypotenuese sides of a right triangle. This of course made him hungry.

Sohcahtoa measured the angle between the 2 forks in the river, and discovered that they were 30 degrees.

Sundown occurred in 10 hours. Would Sohcahtoa make it in time?!?

Thus, Sohcahtoa knew he'd be able to save the camp!!!

Sohcahtoa's brains again saved the day. As a result, the Algebra tribe awarded Sohcahtoa with a nice parcel of land to build a teepee.

After hours pondering where he was going to place his hot tub, Sohcahtoa suddenly discovered that the opposite side of a right triangle has a special relationship with the adjacent side. Since he was dealing with the tanned pelts, he refered to the relationship as tangent.

Through observations of the tribe's teepees, Sohcahtoa learned that the tanned pelts that the Algebra use to cover their teepees are not completely water resistant.

However, if the angle is too steep, the teepee will have no useable space.

Sohcahtoa learned from the TV show, "This Old Teepee" that the optimum angle for a teepee for both space and water runoff is 59 degrees.

Since the standard teepee height is 10 feet, Sohcahtoa needed to determine the area of carpet needed for his home, using the optimum teepee angle.

The problem was that the Algebra tribe was notorious for constructing leaky teepees.

If the angle the wall of the teepee makes with the ground is too flat, the rain will cling on the tanned pelts for too long and leak.

Thus, Sohcahtoa learned that he needed 113 square feet of shag carpeting for his teepee.

Moreover, Sohcahtoa knew his teepee would be spacious and dry!

While waiting for his loan paperwork to go through, Sohcahtoa learned that a special relationship existed between the ratio of the adjacent side and the hypotenuese of a right triangle. He called this relationship, cosine, paying homage to both his father's generosity and his defeat of the Sine.

What was the longest canoe that would fit through the river bend if the widest portion of the river bend was 12 feet, and the angle made from the apex of the curve downstream was 42 degrees?

Sohcahtoa wants the longest canoe that can still make the tight squeeze around the hairpin bend in the river.

**Who will cosine my loan?**

For his valor and wisdom in saving his people from the Sine, Sohcahtoa's father, the chief of the Algebra tribe, agrees to co-sign a loan for him for the newest model of canoe.

Thus, Sohcahtoa knew that any canoe less than 16.14 feet in length would navigate the hairpin river bend.

The chief continued, "When you battled the fierce Sine, you discovered the relationship between the opposite side and hypotenuese of a triangle. The first three letters of your name are a reminder of this special relationship SOH (Sine-Opposite-Hypotenuese).

**What's in a name?**

The Chief said "Son, you questioned your name many years ago. Do you remember?"

**The End**

Sohcahtoa replied "Yes father, but the meaning of my name was never revealed."

The Chief stated "Your name is a combination of the special triangle relationships you have observed."

Weakening, the chief went on, "When you selected a canoe and I co-signed your loan, you discovered the relationship between the adjacent side and the hypotenuese of a right triangle. The second three letter set of your name are a reminder of this special relationship CAH (Cosine-Adjacent-Hypotenuese).

Fading, the chief continued, "When you solved our tanned-pelt, leaky teepee problem, you discovered the relationship between the opposite and adjacent side of a right triangle. The last three letter set of your name are a reminder of this special relationship TOA (Tangent-Opposite-Adjacent).

With his last breath, the chief said "Always remember what your name means, and lead the Algebra tribe to greatness!"