A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $15$ $15$ , what is the largest possible area of the triangle?

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A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $15$ $15$ , what is the largest possible area of the triangle?

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Answer 1 · 2016-11-14T02:43:25

$A = 112.5$ $A = 112.5$

Explanation:

Let $∠ A = \frac{π}{4}$ $angle A = pi/4$

Let $∠ B = \frac{π}{2}$ $angle B = pi/2$

Then $∠ C = π - \frac{π}{2} - \frac{π}{4}$ $angle C = pi - pi/2 - pi/4$

$∠ C = \frac{π}{4}$ $angle C = pi/4$

Please observe that is this is an isosceles right triangle. If we choose the side that is length 15 to be the side opposite $∠ A$ $angle A$ , then the side opposite $∠ C$ $angle C$ must also be length 15 and these sides are the base and the height of the right triangle. Therefore, the area is:

$A = \frac{1}{2} (15) (15)$ $A = 1/2(15)(15)$

$A = 112.5$ $A = 112.5$

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A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $15$ $15$ , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of π4 pi / 4 and π2 pi / 2 . If one side of the triangle has a length of 1515 , what is the largest possible area of the triangle?

1 Answer

Explanation:

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A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{π}{2}$ $pi / 2$ . If one side of the triangle has a length of $15$ $15$ , what is the largest possible area of the triangle?