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3 years ago

1/6 divided by 6 by 6

Mathematics

2 answers:

Ahat [919]3 years ago

7 0

the answer is 1/216

hope this might of helped :/

Alex_Xolod [135]3 years ago

3 0

The answer would be 1/216.

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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

Area of 16+8×+×^2meters. What is the side length

wolverine [178]

Answer:

x +4

Step-by-step explanation:

The trinomial x² +8x +16 is a perfect square trinomial, so factors as ...

x² +8x +16 = (x +4)²

Assuming the side length is one of the factors of the given area, it will be ...

side length = (x +4)

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3 years ago

1. Write down the solution set for each system with variables x, y, and z. zi cexo

insens350 [35]

Answer: need point so HA!

Step-by-step explanation:

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3 years ago

Suppose f(x) = 12x – 1,400 and g(x) = 12x – 1,535. Describe the transformation of the graph of f to the graph of g. Group of ans

m_a_m_a [10]

The graph is translates down 135 units, because you can see how the y-intercept decreased by 135 units from f(x) to g(x).

3 0

3 years ago

1. Which ratios form a proportion? a. 4/9, 12 / 25 b. 3 / 7, 18 / 42 c. 5/11, 20/45 d. 5/8, 15/25. 2. Which ratio forms a propor

harkovskaia [24]

I am pretty sure that the right answer for the first question which is being asked is the second option - <span><span>b. 3 / 7, 18 / 42
</span>What about the next one, I bet it's </span> d. 60 / 100. 3
And the last one is a. 5/8=15/24

4 0

3 years ago

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