Since the garden is symmetric left to right, we can deal with just the left half

Question

Since the garden is symmetric left to right, we can deal with just the left half of it now, then double the result. The diagram shows exactly half of the garden. I've labeled the angle between the two adjacent fence pieces 2x", and given you a nice-sized hint with the dotted lines. Your job is twofold. First, using trig, construct an expression for the area of the three triangles shown, based only on the length 10 10 10 and the angle x. ..then double your expression so it covers both halves of the garden, Second, maximize your expression to find the angle between the fence pieces Task 5 (6pts): Give a function g for the area of the garden in terms of angle x. Remember to double. Also, simplify your result as much as possible (you should be able to get it down to at most two terms). Task 6 (2pts): For which value of x is g(x) maximized? If necessary, round to the tenths' place Task 7 (2pts): What is the maximum area of the garden for this x value? We did it! Now your job is to put it into a picture.. Task 8 (Spts): Label each of the 5 angles in the garden diagram, so that the area is maximized.5 10 feet 10 feet 10 feet 10 feet So there you have it, Trig helped us to increase the area of our garden by approximately 10%! (if that didnt happen for you, go back and check!)

Explanation / Answer

We know that sum of three angles of a triangle = A +B +C

Given that 2x = 120

so angel between of two adjecent sides is half of 120

x=120/2

=60

we know cos60=base/hypo

so cos 45=b/10

sin60= h/10

so area of upper triangle =1/2 *b *h

= 1/2 *2b *h  

=b * h =100 cos60 *100 sin60

by calculation area of upper triangle is 43.25 sq unit

area of lower triangle is 2 * 43.25 = 86.50

so area of hole garden is 2 *86.50 =173 sq unit

solution II

ANGLES A=120

ANGLE B= ANGLE C=ANGLE D=ANGLE D= 60

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