Mathematics, 09.07.2019 11:00 yay47

Asurveyor took the following measurements from two irregularly shaped pieces of land. some of the lengths and angle measures are missing. find all missing lengths and angle measures. round lengths to the nearest tenth and angle measures to the nearest minute

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Answer from: Jc8777

Part A:

To find angle D, we make use of the rule of Sines because we know the measure of the side opposite angle D and we also know the meansure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle D as follows:

$\frac{62}{\sin{D}} = \frac{51}{\sin{53^o}} \\ \\ \Rightarrow \sin{D}= \frac{62\sin{53^o}}{51}} \\ \\ = \frac{49.5154}{51} =0.9709 \\ \\ \Rightarrow D=\sin^{-1}{0.9709} \\ \\ =76.14^o=76^o8'$

Therefore, angle D is 76°8'

Part B:

To find angle E, recall that the sum of the angles in a triangle is 180°.

Thus, 53° + 76°8' + E = 180°

E = 180° - 53° - 76°8' = 50°52'

Therefore, angle E is 50°52'

Part C:

To find the measure of side e, we apply the cosine rule as follows:

$e^2=51^2+62^2-2(51)(62)\cos{50^o52'} \\ \\ =2,601+3,844-2,098.85=3,991.25 \\ \\ \Rightarrow e=\sqrt{3,991.25}=63.18$

Therefore, the measure of side e is 63.2

Part D

To find angle G, we make use of the rule of Sines because we know the measure of the side opposite angle G and we also know the measure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle G as follows:

$\frac{80}{\sin{G}} = \frac{62}{\sin{49^o}} \\ \\ \Rightarrow \sin{G}= \frac{80\sin{49^o}}{62} \\ \\ = \frac{60.3768}{62} =0.9738 \\ \\ \Rightarrow G =\sin^{-1}{0.9738}=76.86^o=76^o52'$

Therefore, angle G is 76°52'

Part E:

To find angle H, recall that the sum of the angles in a triangle is 180°.

Thus, 49° + 76°52' + H = 180°

H = 180° - 49° - 76°52' = 54°14'

Therefore, angle H is 54°14'

Part F:

To find the measure of side a, we apply the cosine rule as follows:

$a^2=80^2+62^2-2(80)(62)\cos{54^o14'} \\ \\ =6,400+3,844-5,798.10=4,445.90 \\ \\ \Rightarrow a=\sqrt{4,445.90}=66.68$

Therefore, the measure of side a is 66.7

Part G:

To find angle A, we make use of the rule of Sines because we know the measure of the side opposite angle A and we also know the measure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle A as follows:

$\frac{66.7}{\sin{A}}
 = \frac{30}{\sin{25^o54'}} \\ \\ \Rightarrow \sin{A}= 
\frac{66.7\sin{25^o54'}}{30} \\ \\ = \frac{29.1347}{30} =0.9712 \\ \\ 
\Rightarrow A =\sin^{-1}{0.9712}=76.21^o=76^o12'$

Therefore, angle A is 76°12'

Part H:

To find angle B, recall that the sum of the angles in a triangle is 180°.

Thus, 25°54' + 76°12' + B = 180°

B = 180° - 25°54' - 76°12' = 77°53'

Therefore, angle B is 77°53'

Part I:

To find the measure of side b, we make use of the rule of sines

Thus, we find side b as follows:

$\frac{b}{\sin{77^o53'}} = \frac{30}{\sin{25^o54'}} \\ \\ 
\Rightarrow b= \frac{30\sin{77^o53'}}{\sin{25^o54'}} \\ \\ = 
\frac{29.3317}{0.4368} =67.15$

Therefore, the measure of side b is 67.2

Answer from: Quest

You would plot 83 on the 83 line and you would plot -113 on the -113 line.

Answer from: Quest

i dont know sorry

step-by-step explanation:

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Asurveyor took the following measurements from two irregularly shaped pieces of land. some of the le...