What is the answer to this question.

\angle DAC=\angle BAD∠DAC=∠BADangle, D, A, C, equals, angle, B, A, D.
What is the length of \overline{BD}
BD
start overline, B, D, end overline?
Round to one decimal place.

Step-by-step explanation:

It can be seen from the diagram that ΔDAC and ΔABD are right angled triangle.

Using the SOH, CAH, TOA trigonometry identity on ΔDAC where;

AC is the hypotenuse = 5.1

CD is the opposite (since it faces the angle directly)

According to SOH;

Sin = opp/hyp

sin

∠DAC = ∠BAD = 38.9°

According to ΔABD, the opposite side is DB which is unknown and the hypotenuse id AB i.e 5.7

Using SOH;

BD ≈ 3.6 to one dp

$4034.40

the perimeter of the field is the sum of the lengths of the four sides:

47 yd + 158 yd + 47 yd + 158 yd = 410 yd

the cost of 3 ft (1 yd) of fence is 3×$3.28 = $9.84.

so the cost of jake's wood perimeter fance is

(410 yd) × ($9.84 /yd) = $4034.40