In the right triangle shown, AC = BC = AC.
What is AB?
We know the length of each leg, and want to find the length of the hypotenuse. What mathematical relationship is there between a right triangle's leg and its hypotenuse?
\qquad AC^2 + BC^2 = x^2
\qquad AC^2 + AC^2 = x^2
\qquad x^2 = 2 \cdot AC^2
\qquad x = \sqrt{2 \cdot AC^2}
\qquad x = \sqrt{2} \cdot \sqrt{AC^2}
\qquad x = AC\sqrt{2}
In the right triangle shown, AC = BC and AB = AB.
How long are each of the legs?
We know the length of the hypotenuse, and want to find the length of each leg. What mathematical relationship is there between a right triangle's legs and its hypotenuse?
\qquad x^2 + x^2 = AB^2
\qquad 2 \cdot x^2 = AB^2
\qquad x^2 = AB * AB / 2
\qquad x = \sqrt{AB * AB / 2}
\qquad x = \sqrt{AB * AB / 4 \cdot 2}
\qquad x = \sqrt{AB * AB / 4} \cdot \sqrt{2}
\qquad x = AB/2 \sqrt{2}
In the right triangle shown, AC = BC and AB = AB\sqrt{2}.
How long are each of the legs?
We know the length of the hypotenuse, and want to find the length of each leg. What mathematical relationship is there between a right triangle's legs and its hypotenuse?
\qquad x^2 + x^2 = AB^2
\qquad 2 \cdot x^2 = (AB\sqrt{2})^2
\qquad 2 \cdot x^2 = AB^2 \cdot (\sqrt{2})^2
\qquad 2 \cdot x^2 = AB * AB \cdot 2
\qquad x^2 = AB * AB
\qquad x = AB
In the right triangle shown, mAB and BC = BC + BCrs.
How long is AB?
We know the length of a leg, and want to find the length of the hypotenuse.
What is the relationship between the sides of a 30 - 60 - 90 triangle?
This is a 30-60-90 triangle with a hypotenuse of length 1.
The ratio of AB : BC is 1 : \dfrac{1}{2}.
Therefore, \dfrac{x}{BC + BCrs} = \dfrac{1}{\frac{1}{2}} = 2.
x = 2 \cdot BC + BCrs
x = BC * 2 + BCrs
In the right triangle shown, mAB and AC = AC + ACrs.
How long is AB?
We know the length of a leg, and want to find the length of the hypotenuse.
What is the relationship between the sides of a 30 - 60 - 90 triangle?
This is a 30-60-90 triangle with a hypotenuse of length 1.
The ratio of AB : AC is 1 : \dfrac{\sqrt{3}}{2}.
Therefore, \dfrac{x}{AC + ACrs} = \dfrac{1}{\frac{\sqrt{3}}{2}} = \dfrac{2}{\sqrt{3}}.
x = \dfrac{2}{\sqrt{3}} \cdot AC + ACrs
x = \dfrac{2 * AC}{\sqrt{3}}
x = \dfrac{2 * AC}{\sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}}
x = \dfrac{2 * AC \cdot \sqrt{3}}{3}
So, x = ABs.
In the right triangle shown, mAB and AB = 2 * BC + BCrs.
How long is BC?
We know the length of the hypotenuse, and want to find the length of the shortest side.
What is the relationship between the sides of a 30 - 60 - 90 triangle?
This is a 30-60-90 triangle with a hypotenuse of length 1.
The ratio of BC : AB is \dfrac{1}{2} : 1.
Therefore, \dfrac{x}{ABdisp} = \dfrac{1}{2}.
x = BC + BCrs
In the right triangle shown, mAB and AB = ABs.
How long is AC?
We know the length of the hypotenuse, and want to find the length of the longest side.
What is the relationship between the sides of a 30 - 60 - 90 triangle?
This is a 30-60-90 triangle with a hypotenuse of length 1.
The ratio of AC : AB is \dfrac{\sqrt{3}}{2} : 1.
Therefore, \dfrac{x}{ABs} = \dfrac{\sqrt{3}}{2}.
x = \dfrac{\sqrt{3}}{2} \cdot ABs
x = AC / 3 \cdot \sqrt{3} \cdot \sqrt{3}
So, x = AC + ACrs.