Question

Triangle ABC is a sketch of a triangular flower bed that has an area of 65.1 square feet. Trigonometric area formula: Area = To the nearest foot, what amount of fencing is needed to surround the perimeter of the flower bed? 17 feet 33 feet 40 feet 50 feet

Answer 1

Answer:

The amount of fencing needed to surround the perimeter of the flower bed is 40 feet

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the length side b

Applying the law of cosines

$c^2=a^2+b^2-2(a)(b)cos(C)$

where

$c=13\ ft\\a=10\ ft\\C=50^o$

substitute

$13^2=10^2+b^2-2(10)(b)cos(50^o)$

solve for b

$169=100+b^2-(20b)cos(50^o)$

$b^2-[20cos(50^o)]b-69=0$

$b^2-12.86b-69=0$

solve the quadratic equation by graphing

The solution is b=16.9 ft

see the attached figure

step 2

Find the perimeter of triangle ABC

$P=AB+BC+AC$

substitute the given values

$P=13+10+16.9=39.9\ ft$

Round to the nearest foot

$P=40\ ft$

therefore

The amount of fencing needed to surround the perimeter of the flower bed is 40 feet

Answer 2

Answer:

c 40 ft

Step-by-step explanation: