1.7 miles: subtract 1.5 from 3.2 which equals 1.7 (make sure to line up the decimals!)
The answer
the sum of the angles in a triangle is always 180°
m < B + m < A + m < C = 180°,
let's find m < B,
by applying sinus rule
14/sinB=10/sinC, so sinB= 10xsinB = 14 x sinC and therefore,
sinB=( 14/10 )sinC =7/2 sin 36° =0.82, so arcsinB=55.08°
the answer is C 55.4°
V=(4/3)(pi)(r^3)
A=4(pi)(r^2)
36(pi)=4(pi)(r^2)
36=4(r^2)
9=(r^2)
r=3
V=(4/3)(pi)(3^3)
V=(4/3)(pi)(27)
V=36(pi)
Answer:
sin θ/2=5√26/26=0.196
Step-by-step explanation:
θ ∈(π,3π/2)
such that
θ/2 ∈(π/2,3π/4)
As a result,
0<sin θ/2<1, and
-1<cos θ/2<0
tan θ/2=sin θ/2/cos θ/2
such that
tan θ/2<0
Let
t=tan θ/2
t<0
By the double angle identity for tangents
2 tan θ/2/1-(tanθ /2)^2 = tanθ
2t/1-t^2=5/12
24t=5 - 5t^2
Solve this quadratic equation for t :
t1=1/5 and
t2= -5
Discard t1 because t is not smaller than 0
Let s= sin θ/2
0<s<1.
By the definition of tangents.
tan θ/2= sin θ/2/ cos θ/2
Apply the Pythagorean Algorithm to express the cosine of θ/2 in terms of s. Note the cos θ/2 is expected to be smaller than zero.
cos θ/2 = -√1-(sin θ/2)^2 = - √1-s^2
Solve for s.
s/-√1-s^2 = -5
s^2=25(1-s^2)
s=√25/26 = 5√26/26
Therefore
sin θ/2=5√26/26=0.196....
