In the right triangle shown, `AC = BC = `

. What is `AC``AB`

?

betterTriangle( 1, 1, "A", "B", "C", AC, AC, "?" );

This is a 45-45-90 triangle because the two legs are congruent.

Thus, the hypotenuse is `\sqrt{2}`

times as long as each of the legs.

`AB = `

`AC`\sqrt{2}

In the right triangle shown, `AC = BC`

and `AB = `

. How long are each of the legs?`AB`

betterTriangle( 1, 1, "A", "B", "C", "?", "?", AB );

This is a 45-45-90 triangle because the two legs are congruent.

Thus, each leg is `\frac{1}{\sqrt{2}}`

times as long as the hypotenuse.

`AC = BC = \frac{1}{\sqrt{2}} `

`AB` = `AB / 2` \sqrt{2}

In the right triangle shown, `AC = BC`

and `AB = `

. How long are each of the legs?`AB`\sqrt{2}

betterTriangle( 1, 1, "A", "B", "C", "?", "?", AB + "\\sqrt{2}" );

This is a 45-45-90 triangle because the two legs are congruent.

Thus, each leg is `\frac{1}{\sqrt{2}}`

times as long as the hypotenuse.

`AC = BC = \frac{1}{\sqrt{2}} `

`AB` \sqrt{2} = `AB`

In the right triangle shown,

and `mAB``BC = `

. How long is `BC + BCrs``AB`

?

betterTriangle( 1, sqrt(3), "A", "B", "C", BC + BCrs, "", "?" );

This is a 30-60-90 triangle.

Thus, the hypotenuse is twice as long as the shorter leg.

`AB = 2 \cdot BC = 2 \cdot (`

`BC + BCrs`) = `( 2 * BC ) + BCrs`

In the right triangle shown,

and `mAB``AC = `

. How long is `AC + ACrs``AB`

?

betterTriangle( 1, sqrt(3), "A", "B", "C", "", AC + ACrs, "?" );

This is a 30-60-90 triangle.

Thus, the hypotenuse is `\frac{2}{\sqrt{3}}`

times as long as the longer leg.

`AB = \frac{2}{\sqrt{3}} \cdot AC = \frac{2}{\sqrt{3}} \cdot (`

`AC + ACrs`) = `ABs`

In the right triangle shown,

and `mAB``AB = `

. How long is `( 2 * BC ) + BCrs``BC`

?

betterTriangle( 1, sqrt(3), "A", "B", "C", "?", "", ( 2 * BC ) + BCrs );

This is a 30-60-90 triangle.

Thus, the shorter leg is half as long as the hypotenuse.

`BC = \frac12 \cdot AB = \frac12 \cdot (`

`( 2 * BC ) + BCrs`) = `( BC ) + BCrs`

In the right triangle shown,

and `mAB``AB = `

. How long is `ABs``AC`

?

betterTriangle( 1, sqrt(3), "A", "B", "C", "", "?", ABs );

This is a 30-60-90 triangle.

Thus, the longer leg is `\frac{\sqrt{3}}{2}`

times as long as the hypotenuse.

`AC = \frac{\sqrt{3}}{2} \cdot AB = \frac{\sqrt{3}}{2} \cdot (`

`ABs`) = `AC + ACrs`