In triangle LaTeX: ABCA B C, the measure of angle LaTeX: AA is LaTeX: 40^\circ40 ∘. Give possible measures for angles LaTeX: BB and LaTeX: CC if triangle LaTeX: ABCA B C is isosceles. Give possible measures for angles LaTeX: BB and LaTeX: CC if triangle LaTeX: ABCA B C is right.

Step-by-step explanation:

An isosceles triangle is a triangle that has two of its sides and angles to be equal.

Given triangle ABC with <A = 40

Note that the sum of angle in a triangle is 180

<A + <B + <C =180

Since the base angle are the same, hence <B = <C

<A+<B +<B = 180

40+2<B = 180

2<B = 140

<B = 140/2

<B = 70

Since <B = <C, hence <C = 70

If triangle ABC is right angled triangle, this means that one of the angle is 90.

Since <A = 40 and one of the other two angle is 90, the third angle will be:

<A+<B<C = 180

40+90+<C = 180

130+<C = 180

<C = 180 - 130

<C = 50

Hence the possible measure of other angles will be 90° and 50°

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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