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
c = 18
b = ?
b/0.7314 = 18/0.4695
Cross multiply
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)
Answer:
9
Step-by-step explanation:
The reciprocal of 1/9 is 9/1 which is just 9.
Answer with Step-by-step explanation:
a.
Taking both sides log
Using identity:
Using identity:
b.
We know that
Using identity
c.
Substitute the values then we get
By using 
Hence, 
Answer:
t=7,t=0
Step-by-step explanation:
2t^2-14t+3=3
Subtract 3 from both sides
2t^2 - 14t +3 - 3 = 3-3
Simpilfy
2t^2 -14t = 0
Answer:
(2l + 2w) + (a + b + c)
Step-by-step explanation:
The formula for the perimeter of a rectangle is
P = 2l + 2w
so if you substitute, it becomes
P = 2(12) + 2(2)
= 24 + 4
= 28
For the perimeter of a triangle the correct formula would be
P = a + b + c
The missing side in the triangle is 3 because 15 - 12 is 3.
If you substitute, it becomes
P = 2 + 3 + 6
P = 11
If we add both perimeters together we get the full perimeter of the figure which is
28 + 11 = 39
I am not sure if you wanted the answer as well but just in case :)
