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3 years ago

Can some one help me on 11 Please

Mathematics

1 answer:

AlexFokin [52]3 years ago

6 0

This is true because 2/5 = 4/10
If u gave 1/10 of a pizza to 6 friends then you would have given them 6/10 of your pizza and have 4/10 left over because 4/10 + 6/10 = 10/10 or 1
Hope this helped :)

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The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 deg

julia-pushkina [17]

Answer:

Approximately $101\; \rm ft$ (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Let $\rm O$ denote the observer.
Let $\rm A$ denote the top of the tree.
Let $\rm R$ denote the base of the tree.
Let $\rm B$ denote the point where line $\rm AR$ (a vertical line) and the horizontal line going through $\rm O$ meets. $\angle \rm B\hat{A}R = 90^\circ$ .

Angles:

Angle of elevation of the base of the tree as it appears to the observer: $\angle \rm B\hat{O}R = 51^\circ$ .
Angle of elevation of the top of the tree as it appears to the observer: $\angle \rm B\hat{O}A = 57^\circ$ .

Let the length of segment $\rm BR$ (vertical distance between the base of the tree and the base of the hill) be $x\; \rm ft$ .

The question is asking for the length of segment $\rm AB$ . Notice that the length of this segment is $\mathrm{AB} = (x + 20)\; \rm ft$ .

The length of segment $\rm OB$ could be represented in two ways:

In right triangle $\rm \triangle OBR$ as the side adjacent to $\angle \rm B\hat{O}R = 51^\circ$ .
In right triangle $\rm \triangle OBA$ as the side adjacent to $\angle \rm B\hat{O}A = 57^\circ$ .

For example, in right triangle $\rm \triangle OBR$ , the length of the side opposite to $\angle \rm B\hat{O}R = 51^\circ$ is segment $\rm BR$ . The length of that segment is $x\; \rm ft$ .

$\begin{aligned}\tan{\left(\angle\mathrm{B\hat{O}R}\right)} = \frac{\,\rm {BR}\,}{\,\rm {OB}\,} \; \genfrac{}{}{0em}{}{\leftarrow \text{opposite}}{\leftarrow \text{adjacent}}\end{aligned}$ .

Rearrange to find an expression for the length of $\rm OB$ (in $\rm ft$ ) in terms of $x$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{BR}}{\tan{\left(\angle\mathrm{B\hat{O}R}\right)}} \\ &= \frac{x}{\tan\left(51^\circ\right)}\approx 0.810\, x\end{aligned}$ .

Similarly, in right triangle $\rm \triangle OBA$ :

$\begin{aligned}\mathrm{OB} &= \frac{\mathrm{AB}}{\tan{\left(\angle\mathrm{B\hat{O}A}\right)}} \\ &= \frac{x + 20}{\tan\left(57^\circ\right)}\approx 0.649\, (x + 20)\end{aligned}$ .

Equate the right-hand side of these two equations:

$0.810\, x \approx 0.649\, (x + 20)$ .

Solve for $x$ :

$x \approx 81\; \rm ft$ .

Hence, the height of the top of this tree relative to the base of the hill would be $(x + 20)\; {\rm ft}\approx 101\; \rm ft$ .

6 0

3 years ago

Solving proportions<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%5C3%7D%7B5%7D%20%20%3D%20%20%5Cfrac%7Ba%7D%7B20%7D%20" i

Olegator [25]

Answer:

a = 4/3

Step-by-step explanation:

1/3 a

----- = -----

5 20

Using cross products

1/3 * 20 = 5a

20/3 = 5a

Divide each side by 5

20/3 * 1/5 = 5a/5

4/3 = a

8 0

3 years ago

Help plz!! Will mark brainliest!

Roman55 [17]

Answer: point Q is located in (3,4)

Step-by-step explanation: the ratio of SQ:QT is 5:2, and for every two units (up two, right two) it is one ratio. go up two, right two five times that leads a ratio between 5:2.

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3 years ago

Which equation can be used to find the number of deer in the forest on January 1? A zoologist is recording the loss of deer in a

Vanyuwa [196]

The equation would be d - 19 = 73. So the zoologist would take the number of deer recorded and subtract it from 19 (since it said 19 fewer deer) and the answer would be 73 (because that is how many deer were recorded a year later. I hope this helps!

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4 years ago

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