Answer:
<em>1,760 actual miles separate Springfield from Glenview.</em>
Step-by-step explanation:
<u>Scaling</u>
Objects can be represented in a reduced or augmented size by using scaling which is basically multiplying or dividing real dimensions by a constant factor. We use scaling when representing geographic locations on a map.
The map has the scale:
0.75 inch => 220 miles
This gives us the scaling factor as 220/0.75. There is no need to divide.
We are given the distance from Springfield to Glenview is 6 inches on the map. The actual distance is
6*220/0.75 = 1,760
1,760 actual miles separate Springfield from Glenview.
The complete question in the attached figure
we have that
tan a=7/24 a----> III quadrant
cos b=-12/13 b----> II quadrant
sin (a+b)=?
we know that
sin(a + b) = sin(a)cos(b) + cos(a)sin(b<span>)
</span>
step 1
find sin b
sin²b+cos²b=1------> sin²b=1-cos²b----> 1-(144/169)---> 25/169
sin b=5/13------> is positive because b belong to the II quadrant
step 2
Find sin a and cos a
tan a=7/24
tan a=sin a /cos a-------> sin a=tan a*cos a-----> sin a=(7/24)*cos a
sin a=(7/24)*cos a------> sin²a=(49/576)*cos²a-----> equation 1
sin²a=1-cos²a------> equation 2
equals 1 and 2
(49/576)*cos²a=1-cos²a---> cos²a*[1+(49/576)]=1----> cos²a*[625/576]=1
cos²a=576/625------> cos a=-24/25----> is negative because a belong to III quadrant
cos a=-24/25
sin²a=1-cos²a-----> 1-(576/625)----> sin²a=49/625
sin a=-7/25-----> is negative because a belong to III quadrant
step 3
find sin (a+b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin a=-7/25
cos a=-24/25
sin b=5/13
cos b=-12/13
so
sin (a+b)=[-7/25]*[-12/13]+[-24/25]*[5/13]----> [84/325]+[-120/325]
sin (a+b)=-36/325
the answer issin (a+b)=-36/325
Answer:16
Step-by-step explanation:dsbwdb
let
(hypotenuse ) c = 10 in
(perpendicular) a = 8 in
(base) b =?
By using Pythagoras theorem
c^2= a^2+b^2
(10)^2 = (8)^2 +(b)^2
100 = 64 +(b)^2
100- 64 = (b)^2
36 = (b)^2
√36 = b
6 = b
hence b= 6 in
The missing side would be B = 15