Home > Geometry > Perimeter and Area of Triangle

A triangle has two corners with angles of # pi / 4 # and # pi / 2 #. If one side of the triangle has a length of #3 #, what is the largest possible area of the triangle?

Answer 1

Largest possible area of triangle #A_t = color(green)(4.5# sq. units

Given #hatA = pi/2, hatB = pi / 4

Third angle #hatC = pi - pi/2 - pi/4 = pi/4#

It's a right isosceles triangle.

To get the largest area of the triangle, length 3 should be equated to the side opposite to the least angle (#pi/4#, in this case).

Area of triangle #A_t = (1/2) b c# where b = c = 3.

#:.# Largest possible area #A_t = (1/2) * 3 * 3 = 9/2 = color(green)(4.5# sq. units

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

Answer 2

Theodore Abad

To find the largest possible area of the triangle, you can use the formula for the area of a triangle, which is 1/2 * base * height. Since one side of the triangle has a length of 3, and the angles are π/4 and π/2, you can use trigonometric ratios to find the lengths of the other sides. Then, you can calculate the area of the triangle using the formula.

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.