A triangle has two corners with angles of $\frac{π}{2}$ $( pi ) / 2$ and $\frac{π}{6}$ $( pi )/ 6$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{2}$ $( pi ) / 2$ and $\frac{π}{6}$ $( pi )/ 6$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-01-06T01:46:18

$A = \frac{1}{2} (2) (2 \sqrt{3}) = 2 \sqrt{3}$ $A=1/2(2)(2sqrt3)=2sqrt3$ sq units

Explanation:

There is a kind of triangle that in degree format is called a 30-60-90 triangle (and so would have angles of $\frac{π}{2}, \frac{π}{3}, \frac{π}{6}$ $pi/2, pi/3, pi/6$ . The ratio of the sides of this kind of a triangle are 1, $\sqrt{3}$ $sqrt3$ , 2.

If we take the length of 2 and assign that to the shortest side, then we'll have sides of 2, $2 \sqrt{3}$ $2sqrt3$ , 4.

The area of a triangle is found by:

$A = \frac{1}{2} b h$ $A=1/2bh$

and so our triangle is:

$A = \frac{1}{2} (2) (2 \sqrt{3}) = 2 \sqrt{3}$ $A=1/2(2)(2sqrt3)=2sqrt3$ sq units

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A triangle has two corners with angles of $\frac{π}{2}$ $( pi ) / 2$ and $\frac{π}{6}$ $( pi )/ 6$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of π2 ( pi ) / 2 and π6 ( pi )/ 6 . If one side of the triangle has a length of 22 , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{2}$ $( pi ) / 2$ and $\frac{π}{6}$ $( pi )/ 6$ . If one side of the triangle has a length of $2$ $2$ , what is the largest possible area of the triangle?