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Ber [7]
1 year ago
13

Find the length of side AB. Give your answer to 1 decimal place. 12 cm 62° A B

Mathematics
1 answer:
VladimirAG [237]1 year ago
4 0

Hey there!

To solve this problem, we will be using Trigonometric Ratio. Trigonometry is always helpful when it comes to finding a missing side with specific measure/angle.

1. Cosine Ratio

  • Currently, there are 6 Trigonometric Ratios. But we will be talking about Cosine Ratio instead since it is what we will be using in your question! Cosine Ratio is defined as <u>a</u><u>d</u><u>j</u><u>a</u><u>c</u><u>e</u><u>n</u><u>t</u><u> </u><u>t</u><u>o</u><u> </u><u>h</u><u>y</u><u>p</u><u>o</u><u>t</u><u>e</u><u>n</u><u>u</u><u>s</u><u>e</u><u> </u><u>o</u><u>r</u><u> </u><u>a</u><u>d</u><u>j</u><u>a</u><u>c</u><u>e</u><u>n</u><u>t</u><u>/</u><u>h</u><u>y</u><u>p</u><u>o</u><u>t</u><u>e</u><u>n</u><u>u</u><u>s</u><u>e</u><u>.</u> You know what adjacent and hypotenuse are right? If not then head to the next topic!

2. Adjacent and Hypotenuse

  • Adjacent is basically the base of a triangle. It is basically drawn from right angle to any measure/angles.
  • Hypotenuse is the longest side of a right triangle. It is also an opposite side of right angle.

Hope you understand this topic! If not, feel free to ask!

3. Solve The Problem

  • Since our adjacent is length AB but we don't know its exact value. What we have to do is to determine AB as any variables which I will determine AB as "x".
  • Next, we have the value of hypotenuse which is 12 cm.
  • Then we also know the Cosine Ratio which is adjacent to hypotenuse.

Therefore, the equation for the problem is:

\large{cos62 \degree =  \frac{x}{12} }

<em>*</em><em>c</em><em>o</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>t</em><em>h</em><em>e</em><em> </em><em>s</em><em>h</em><em>o</em><em>r</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em><em>o</em><em>f</em><em> </em><em>c</em><em>o</em><em>s</em><em>i</em><em>n</em><em>e</em><em>*</em>

At this part, we need a calculator to find the value of cos62 degrees. That's because it is not a degree like 0, 30, 45, 60 and 90 which can be found without a calculator.

When we put cos62 in a calculator, make sure to put it in degree mode since a calculator has two modes which are degree and radian.

When we put cos62 in, we should get 0.46947156... Because you want a one decimal place, we round the value up to the nearest tenth as we get 0.5 because 6 is greater than 5 and should be rounded up and not down. That makes the equation to:

\large{0.5 =  \frac{x}{12} }

Oh well! Finally to the equation part. Whenever you have to solve the equation that has decimal numbers in it, the best way to deal with decimal numbers is to make them into a whole number or integer. But how? Simply multiply the whole equation by 10. Because 0.5×10 is 5 thus 0.5 becomes an integer after multiplying 10.

\large{0.5 \times 10 =   \frac{x}{12}  \times 10} \\  \large{5 =  \frac{10x}{12} }

10x/12 can be simplified again.

\large{5 =   \frac{5x}{6} }

Then we isolate x-value by multiplying 6 the whole equation.

\large{5 \times 6 =  \frac{5x}{6}  \times 6} \\  \large{30 = 5x} \\  \large{x = 6}

Huh, that's awkward! We want the answer in a 1 decimal place but seems like the answer for this is 6. Why? Well that is not an exact answer, but more like an approximation. Because the value of cos62 degree is actually a repeating decimal and doesn't have exact value.

When we put the equation cos62 = x/12 in the equation and solve. It appears that the the answer is 5.63365875. Because we round up to nearest tenth, it gives an approximation to 5.63365875 instead.

Hence, the equation and value above is just a rounded to the whole number from 5.63365875.

Because you want a one place decimal. Hence,

4. Final Answer

  • The length AB is 5.6 (rounded to nearest tenth)

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Answer:

150 ft^2

Step-by-step explanation:

The formula is (30*10)/2 which is equal to 150.

3 0
1 year ago
Suppose a movie theater you work at sells popcorn in three different sizes. A small costs $2, a medium costs $5, a large costs $
lidiya [134]

Answer:

\left \{ {{{s+m+l=250}} \atop {2s+5m+10l=1726 \atop {l=2s} \right.

Small popcorns: 68

Medium popcorns:: 46

Large popcorns: 136

Step-by-step explanation:

<h3>The complete exercise is: "Suppose the movie theater you work at sells popcorn in three different sizes. A small costs $2, a medium costs $5, and a large costs $10. On your shift, you sold 250 total containers of popcorn and brought in $1726. You sold twice as many large containers as small ones. How many of each popcorn size did you sell?" </h3><h3 />

Let be "s" the number of small popcorns you sold,  "m" the number of medium popcorns syou sold and "l" the number of large popcorns you sold.

Set up a system of equations:

\left \{ {{{s+m+l=250}} \atop {2s+5m+10l=1726 \atop {l=2s} \right.

 To solve it:

- Multiply the first equation by -5 and add it to the second equation:

\left \{ {{-5s-5m-5l=-1250}} \atop {2s+5m+10l=1726 \right. \\..................................\\-3s+5l=476

- Substitute the third equation  into -3s+5l=476 and solve for "s":

-3s+5(2s)=476\\\\7s=476\\\\s=68

- Substitute this value into the third equation of the system to find "l":

l=2(68)=136

- Substitute the known values into the first equation of the system  and solve for "m" in order to find its value:

68+m+136=250\\\\m=46

8 0
2 years ago
PLEASE PLEASE PLEEEEASE HELP!!!!!! BRAINLIEST!!!!!!!!!
weqwewe [10]

Answer

B

Step-by-step explanation:

On the x axis it starts at zero and ends at 6 so therefore it can be anything inbetween that and 0 and 6

5 0
2 years ago
Find the volume of the three-dimensional figure in terms ofx.
LenaWriter [7]

Answer:

That is 19x16x13

Therefore the answer will be =18928

5 0
2 years ago
HELP ASAP What is the value of x ?
jeka94
The value of x is 5 I hope it helps your welcome

5 0
2 years ago
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