Answer:
(a) x = 30°
(b) mRS = 30°
mST = 120°
mTU = 120°
mUR = 90°
Step-by-step explanation:
(a) In the picture attached, the diagram is shown.
Given that m arc RS = x, from the ratios:
m arc ST = 4x
m arc TU = 4x
m arc UR = 3x
The addition of the four arcs must be equal to 360°, then:
x + 4x + 4x + 3x = 360°
12x = 360°
x = 360°/12 = 30°
(b) m arc RS = x = 30°
m arc ST = 4x = 4*30° = 120°
m arc TU = 4x = 4*30° = 120°
m arc UR = 3x = 3*30° = 90°
Answer:
7. 49
8. 10.4
Step-by-step explanation:
7) our hypotenuse is 8, and the side opposite the base of ladder and ground angle is 6, therefore we can use Sin
sin = opposite/hypotenuse
sin(x) = 6/8 = 3/4
sin-1(3/4) = 49
8) using the theorem that alternate exterior angles are congruent
the angle opposite side x is 30
tan = opposite/adjacent
tan(30) = x/18
x = 18tan(30) = 6√(3) = 10.4
you can also use 30-60-90 special right triangles.
the side opposite 30 is x
side opposite 60 is x√(3)
and side opposite 90 is 2x
<span> I am assuming you want to prove:
csc(x)/[1 - cos(x)] = [1 + cos(x)]/sin^3(x).
</span>
<span>If we multiply the LHS by [1 + cos(x)]/[1 + cos(x)], we get:
LHS = csc(x)/[1 - cos(x)]
= {csc(x)[1 + cos(x)]/{[1 + cos(x)][1 - cos(x)]}
= {csc(x)[1 + cos(x)]}/[1 - cos^2(x)], via difference of squares
= {csc(x)[1 + cos(x)]}/sin^2(x), since sin^2(x) = 1 - cos^2(x).
</span>
<span>Then, since csc(x) = 1/sin(x):
LHS = {csc(x)[1 + cos(x)]}/sin^2(x)
= {[1 + cos(x)]/sin(x)}/sin^2(x)
= [1 + cos(x)]/sin^3(x)
= RHS.
</span>
<span>I hope this helps! </span>
$34.80 because, if you add 15+2+21=58x12.00=696x0.05=34.80
