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A triangle has two corners with angles of # pi / 2 # and # ( pi )/ 8 #. If one side of the triangle has a length of #5 #, what is the largest possible area of the triangle?

Answer 1

Aurora Ayala

Largest possible area of the triangle is 30.1777

Given are the two angles #(pi)/2# and #pi/8# and the length 5

The remaining angle:

#= pi - ((pi)/2) + pi/8) = (3pi)/8#

I am assuming that length AB (1) is opposite the smallest angle.

Using the ASA

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

Area#=( 5^2*sin(pi/2)*sin((3pi)/8))/(2*sin(pi/8))#

Area#=30.1777#

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Answer 2

Sadie Allen

The largest possible area of the triangle is approximately 10.3906 square units.

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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.