Answer:
1. For quadrilateral ABCD:
AB = AD = 2.7, BC = DC = 3.2, and AC = 3.168
<BAC = <DAC
, <ABC = <ADC =
, and <ACB = <ACD = ![50.2^{o}](https://tex.z-dn.net/?f=50.2%5E%7Bo%7D)
2. For quadrilateral ABCE:
AB = EC = 2.7, BC = AE = 3.2, and AC = 3.168
<BAC = <ACE
, <ABC = <AEC =
, and <ACB = <EAC = ![50.2^{o}](https://tex.z-dn.net/?f=50.2%5E%7Bo%7D)
Step-by-step explanation:
Applying the Cosine rule to triangle ABC,
=
+
- 2/AB/ x /BC/ Cos B
=
+
- 2 x 2.7 x 3.2 Cos 64.3
= 7.29 + 10.24 - 17.28 x 0.4337
= 17.53 - 7.49434
= 10.03566
AC = ![\sqrt{10.03566}](https://tex.z-dn.net/?f=%5Csqrt%7B10.03566%7D)
= 3.168
Applying the Sine rule,
=
= ![\frac{c}{Sin C}](https://tex.z-dn.net/?f=%5Cfrac%7Bc%7D%7BSin%20C%7D)
So that:
= ![\frac{3.168}{Sin 643.^{o} }](https://tex.z-dn.net/?f=%5Cfrac%7B3.168%7D%7BSin%20643.%5E%7Bo%7D%20%7D)
= ![\frac{3.168}{0.9011}](https://tex.z-dn.net/?f=%5Cfrac%7B3.168%7D%7B0.9011%7D)
Sin A = ![\frac{3.2 * 0.9011}{3.168}](https://tex.z-dn.net/?f=%5Cfrac%7B3.2%20%2A%200.9011%7D%7B3.168%7D)
= ![\frac{2.88352}{3.168}](https://tex.z-dn.net/?f=%5Cfrac%7B2.88352%7D%7B3.168%7D)
= 0.9102
⇒ A =
0.9102
= ![65.5^{o}](https://tex.z-dn.net/?f=65.5%5E%7Bo%7D)
But sum of angles in a triangle is
, so that;
A + B + C = ![180^{o}](https://tex.z-dn.net/?f=180%5E%7Bo%7D)
65.5 + 64.3 + C = ![180^{o}](https://tex.z-dn.net/?f=180%5E%7Bo%7D)
129.8 + C = ![180^{o}](https://tex.z-dn.net/?f=180%5E%7Bo%7D)
C =
- 129.8
C = ![50.2^{o}](https://tex.z-dn.net/?f=50.2%5E%7Bo%7D)
1. For quadrilateral ABCD:
AB = AD = 2.7, BC = DC = 3.2, and AC = 3.168
<BAC = <DAC
, <ABC = <ADC =
, and <ACB = <ACD = ![50.2^{o}](https://tex.z-dn.net/?f=50.2%5E%7Bo%7D)
2. For quadrilateral ABCE:
AB = EC = 2.7, BC = AE = 3.2, and AC = 3.168
<BAC = <ACE
, <ABC = <AEC =
, and <ACB = <EAC = ![50.2^{o}](https://tex.z-dn.net/?f=50.2%5E%7Bo%7D)