Home > Geometry > Perimeter and Area of Triangle

A triangle has two corners with angles of # pi / 12 # and # (5 pi )/ 8 #. If one side of the triangle has a length of #8 #, what is the largest possible area of the triangle?

Answer 1

Savannah Aguilar

Largest possible area of the triangle is 90.6224

Given are the two angles #(pi)/12# and #(5pi)/8# and the length 8

The remaining angle:

#= pi - ((pi)/12) + (5pi)/8) = (7pi)/24#

I am assuming that length AB (8) is opposite the smallest angle.

Using the ASA

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

Area#=( 8^2*sin((7pi)/24)*sin((5pi)/8))/(2*sin(pi/12))#

Area#=90.6224#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Claire Akin

The largest possible area of the triangle can be found using the formula for the area of a triangle, which is 1/2 * base * height.

First, find the height of the triangle using trigonometric functions: Height = side * sin(angle)

Then, calculate the area using the formula: Area = 1/2 * side * height

Substitute the given values: Height = 8 * sin((5π)/8) Area = 1/2 * 8 * 8 * sin((5π)/8)

Calculate the numerical value of the expression: Area ≈ 30.51 square units.

By signing up, you agree to our Terms of Service and Privacy Policy

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.