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A triangle has two corners with angles of # ( pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #14 #, what is the largest possible area of the triangle?

Answer 1

Theodore Abad

Largest possible area of the triangle is 169.741

Given are the two angles #(pi/3)# and #pi/6# and the length 14

The remaining angle:

#= pi - ((pi)/3) + pi/6) = (pi)/2#

I am assuming that length AB (14) is opposite the smallest angle.

Using the ASA

Area#=(c^2*sin(A)*sin(B))/(2*sin(C))#

Area#=( 14^2*sin((pi)/2)*sin((pi)/3))/(2*sin(pi/6))#

Area#=169.741#

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Answer 2

James Atkins

The largest possible area of the triangle can be calculated using the formula for the area of a triangle, which is 0.5 * base * height. In this case, the given side length of 14 forms the base of the triangle. To find the height, you can use the sine of the angle (π/3) to determine the height corresponding to the opposite side (the side opposite to the angle π/3).

So, the height (h) can be calculated as h = 14 * sin(π/3).

Then, you can use this height to find the area of the triangle using the formula for the area of a triangle.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.