Answer:
282°
Step-by-step explanation:
The measure of long arc KLM can be found by first determining the measure of short arc KM. That arc can be found using the inscribed angle theorem.
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<h3>value of x</h3>
The inscribed angle theorem tells you the measure of arc KM is twice the measure of the inscribed angle KLM that subtends it. This relation can be used to find the value of x, hence the measure of the arc.
2∠KLM = arc KM
2(5x -1) = 8x +14
10x -2 = 8x +14 . . . . . . eliminate parentheses
2x = 16 . . . . . . . . . . add 2-8x
x = 8 . . . . . . . . . divide by 2
<h3>measure of arc KM</h3>
The expression for the measure of arc KM can be evaluated.
arc KM = 8x +14 = 8(8) +14 = 78°
<h3>
measure of arc KLM</h3>
The total of arcs of a circle is 360°, so the measure of long arc KLM will bring the total with arc KM to 360°:
arc KM +arc KLM = 360°
arc KLM = 360° -arc KM
arc KLM = 360° -78° = 282°
The measure are long arc KLM is 282°.
The answer is I believe: 21
In this problem, we can imagine that all the points
connect to form a triangle. The three point or vertices are located on the
pitcher mount, the home plate and where the outfielder catches the ball. So in
this case we are given two sides of the triangle and the angle in between the
two sides.
<span>With the following conditions, we can use the cosine law
to solve for the unknown 3rd side. The formula is:</span>
c^2 = a^2 + b^2 – 2 a b cos θ
Where,
a = 60.5 ft
b = 195 ft
θ = 32°
Substituting the given values:
c^2 = (60.5)^2 + (195)^2 – 2 (60.5) (195) cos 32
c^2 = 3660.25 + 38025 – 20009.7
c^2 = 21,675.56
c = 147.23 ft
<span>Therefore the outfielder throws the ball at a distance of
147.23 ft towards the home plate.</span>
