(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°

read more : link

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)