(50 points) bob is standing 25 feet from a lamppost that is to his left and 30 feet from a lamppost that is to his right. the distance between the two lampposts is 20 feet. what is the measure of the angle formed from the line from each lamppost to bob? approximate to the nearest degree.

point A----------------- > Bob

point B----------------- > lamppost that is to Bob left

point C----------------- > lamppost that is to Bob right

we know that

dAB=25 ft

dAC=30 ft

dBC=20 ft

see the attached figure

we use the law of cosines------------- > dBC²=dAB² +dAC² -2(dAB)(dAC)cos(alfa)

we have that

20²=25² +30² -2(25)(30)cos(alfa)-------- > cos (alfa)=(20²-(25² +30²))/(-2*25*30)

cos (alfa)=(400-(625 +900))/(-1500)= (400-(625 +900))/(-1500)=1125/1500=0.75

alfa=arccos (0.75)=     41.4096 -------- > 41 °-------- > ∡ BAC

 the answer is 41 °

Angle = 41°

The information below forms a triangle. Therefore, lets represent the information with a diagram below.

From the diagram we are to find angle x. Therefore, using cosine rule we can find angle below

400 = 900 + 625 - 1500 cos x

400 - 1525 = -1500 cos x

-1125 = -1500 cos

cos x = -1125/-1500

x = cos⁻¹ 0.75

x = 41.409622109

x ≈ 41°

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step-by-step explanation:

9) i can't see the angle so whatever it is just do this: cos(angle) x hypotenuse and then use that answer and they hypotenuse and plug it into this: (answer you just got)^2 + b^2 = (hypotenuse)^2. the first answer will be the answer of the adjacent side and the second answer after this equation will be the opposite side.

10) y = 14 x = √147 or 12.12435565

11) x = 4.8

12) x = 4.2

13) x = 9.3

14) pq: 13.2

qr : 17.6

angle p: 53º

15) angle c: 54.3º

angle a: 35.7º

16) h = 21040

v = 1841

step-by-step explanation:

10) 7/sin(30) = 14 = y

7^2 + b^2 = 14^2

49 + b^2 = 196

b^2 = 196 - 49

√b^2 = √147

x = √147

11) cos(70) x 14 = 4.788282007

x = 4.8

12) tan(25) x 9 = 4.196768923

x = 4.2

13) sin(31) x 18 = 9.270685348

x = 9.3

14) pq: sin(37) x 22 = 13.23993051

pq: 13.2

qr: cos(37) x 22 = 17.56998122

qr : 17.6

angle p: 180 - (37 + 90) = 53º

15) cos-1(7/12) = 54.31466529

angle c: 54.3º

angle a: 180 - (90 + 54.31466529) = 35.68533471

angle a: 35.7º

16) 4 x 5280 = 21120

cos(5) x 21120

h = 21039.63202

h = 21040

sin(5) x 21120

v = 1840.729287

v = 1841