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3 years ago

An amusement park wants to install a zipline that is 500 feet long and slopes

Mathematics

1 answer:

Mila [183]3 years ago

8 0

Answer:

Check attachment for solution

Step-by-step explanation:

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Please dont ignore, Need help!!! Use the law of sines/cosines to find..

Ket [755]

Answer:

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:

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:

$\sin{A} = \sin{103\textdegree{}}$ ,
The opposite side of angle A $a = BC = 26$ ,
The angle C is to be found, and
The length of the side opposite to angle C $c = AB = 6$ .

$\displaystyle \frac{\sin{C}}{\sin{A}} = \frac{c}{a}$ .

$\displaystyle \sin{C} = \frac{c}{a}\cdot \sin{A} = \frac{6}{26}\times \sin{103\textdegree}$ .

$\displaystyle C = \sin^{-1}{(\sin{C}}) = \sin^{-1}{\left(\frac{c}{a}\cdot \sin{A}\right)} = \sin^{-1}{\left(\frac{6}{26}\times \sin{103\textdegree}}\right)} = 13.0\textdegree{}$ .

Note that the inverse sine function here $\sin^{-1}()$ is also known as arcsin.

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.

For triangle ABC:

$b = 21$ ,
$c = 30$ ,
The length of $a$ (segment BC) is to be found, and
The cosine of angle A is $\cos{123\textdegree}$ .

Therefore, replace C in the equation with A, and the law of cosine will become:

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

$\displaystyle \begin{aligned}a &= \sqrt{b^{2} + c^{2} - 2\;b\cdot c\cdot \cos{A}}\\&=\sqrt{21^{2} + 30^{2} - 2\times 21\times 30 \times \cos{123\textdegree}}\\&=45.0 \end{aligned}$ .

For triangle ABC:

$a = 14$ ,
$b = 9$ ,
$c = 6$ , and
Angle B is to be found.

Start by finding the cosine of angle B. Apply the law of cosine.

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

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

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

For triangle DEF:

The length of segment DF is to be found,
The length of segment EF is 9,
The sine of angle E is $\sin{64\textdegree}}$ , and
The sine of angle D is $\sin{39\textdegree}$ .

Apply the law of sine:

$\displaystyle \frac{DF}{EF} = \frac{\sin{E}}{\sin{D}}$

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

7 0

3 years ago

100+ POINTS <br> Go to my profile for more

VARVARA [1.3K]

Answer:

thanks

Step-by-step explanation:

4 0

2 years ago

Is 3 1/4 closer to 3 or 4<br><br><br>is 3 3/5 closer to 3 or 4

agasfer [191]

Answer:3 and 1/4 is closer to 3 and 3/5 is closer to 4

Step-by-step explanation: one is closer on the number scale then the other

3 0

2 years ago

A store manager determines that, on average, it takes Jemel 26.1 seconds to fold and put away 1 shirt. The manager uses a clock

Furkat [3]

<span>This problem is an example of ratio and proportion. A ratio is a comparison between two different things. You are given the time of about 26.1 seconds to fold 1 shirt. Also you are given 48 shirts. You are required to find the time in seconds to fold 48 shirts. The solution of this problem is,</span>
<span>
26.1 seconds /1 shirt = time/ 48 shirts</span>
<span>time = (48 shirts) (26.1 seconds /1 shirt)</span>
<span>time<u> = 1,252.8 seconds</u></span>
<u>The time it takes to fold 48 shirts is 1,252.8 seconds.</u>

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2 years ago

A bakery sells 6 bagels for $3.99 and 4 muffins for $2.29. What is the total

nignag [31]

$15.96 for bagels, $6.87 for muffins

6 0

2 years ago