Answer:
<B = 47°
<C = 28°
b = AC = 28.0
Step-by-step explanation:
Given:
∆ABC
AB = c = 18
BC = a = 37
<A = 105°
Required:
Length of AC = b
measure of angle B and angle C
SOLUTION:
==>Use the sine rule, sin A/a = sinC/c to find the angle of C:
SinA = sin(105) = 0.9659
a = 37
sinC = ?
c = 18
0.9659/37 = sinC/18
Cross multiply
0.9659*18 = 37*sinC
17.3862 = 37*sinC
Divide both sides by 37
17.3862/37 = sinC
0.4699 = sinC
sinC = 0.4699
C = Sin-¹(0.4699)
C = 28.0° (nearest tenth)
==>Find angle B using sum of angles in a triangle:
Angle B = 180 - (105+28)
Angle B = 180 - 133
Angle B = 47°
==>Find length of b using sine rule, b/sinB = c/sinC:
SinC = sin(28) = 0.4695
SinB = sin(47) = 0.7314
b = ?
b/0.7314 = 18/0.4695
b*0.4695 = 18*0.7314
b*0.4695 = 13.1652
Divide both sides by 0.4695
b = 13.1652/0.4695
b = 28.0 (nearest tenth)
90 miles
There's more than one way in which to do this. I have chosen to convert '180 minutes' to '3 hours.'
Since distance = rate times time, we have here:
distance traveled in 180 minutes = (30 mph)(3 hr) = 90 miles
y= 3w+525
d
by using the a²+b²=c²
c²=
