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2 years ago

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Rick, John, and Kevin are playing catch. Rick throws the ball to John, John throws the ball to Kevin, and Kevin throws the ball

to Rick. John knows that the distance between him and Rick is 20 yards and the distance between him and Kevin is 20 yards. He also knows that the angle created between Rick, himself, and Kevin has a measure of 30°. Which person is making the shortest throw?

1 answer:

pishuonlain [190]2 years ago

6 0

Answer:

Kevin and Rick

Step-by-step explanation:

RJ - 20 y

JK - 20square root 3

M<RJK - 30 y

Let’s find the length segment KR by using law of cosines

KR^2 = RJ^2 + JK^2 - 2(RJ)(JK)cos(<RJK)

KR^2=400

KR=20 yards

Kevin and Rick throwing same distance, but John’s distance is longer.

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16. Angle C is approximately 13.0 degrees.

17. The length of segment BC is approximately 45.0.

18. Angle B is approximately 26.0 degrees.

15. The length of segment DF "e" is approximately 12.9.

Step-by-step explanation:

<h3>16</h3>

By the law of sine, the sine of interior angles of a triangle are proportional to the length of the side opposite to that angle.

For triangle ABC:

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The angle C is to be found, and
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Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

<h3>17</h3>

By the law of cosine,

$c^{2} = a^{2} + b^{2} - 2\;a\cdot b\cdot \cos{C}$ ,

where

$a$ , $b$ , and $c$ are the lengths of sides of triangle ABC, and
$\cos{C}$ is the cosine of angle C.

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The cosine of angle A is $\cos{123\textdegree}$ .

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$a^{2} = b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}$ .

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<h3>18</h3>

For triangle ABC:

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$\displaystyle B = \cos^{-1}{\left(\frac{a^{2} + c^{2} - b^{2}}{2\;a\cdot c}\right)} = \cos^{-1}{\left(\frac{14^{2} + 6^{2} - 9^{2}}{2\times 14\times 6}\right)} = 26.0\textdegree$ .

<h3>15</h3>

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
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$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

$\displaystyle DF = \frac{\sin{E}}{\sin{D}}\cdot EF = \frac{\sin{64\textdegree}}{39\textdegree} \times 9 = 12.9$ .

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