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2 years ago

Solve for x and show work.

Mathematics

2 answers:

mrs_skeptik [129]2 years ago

8 0

Answer:

x = -5

Step-by-step explanation:

Angles "50" and "x+55" are alternate interior angles which means that they are the same.

So 50 = x + 55

That leaves you with x = -5

Feliz [49]2 years ago

7 0

X=-5 pretty sure that’s correct

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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

2 years ago

Simplify <br> cosx ( tanx+cotx)

Soloha48 [4]

The first step to solving this is to use tan(t) = $\frac{sin(t)}{cos(t)}$ to transform this expression.
cos(x) × $( \frac{sin(x)}{cos(x)} + cot(x) )$
Using cot(t) = $\frac{cos(x)}{sin(x)}$ ,, transform the expression again.
cos(x) × $( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )$
Next you need to write all numerators above the least common denominator (cos(x)sin(x)).
cos(x) × $\frac{sin(x)^{2} + cos(x)^{2} }{cos(x)sin(x)}$
Using sin(t)² + cos(t)² = 1,, simplify the expression.
cos(x) × $\frac{1}{cos(x)sin(x)}$
Reduce the expression with cos(x).
$\frac{1}{sin(x)}$
Lastly,, use $\frac{1}{sin(t)}$ = csc(t) to transform the expression and find your final answer.
csc(x)
This means that the final answer to this expression is csc(x).
Let me know if you have any further questions.
:)

4 0

2 years ago

Each letter of the words SEVENTH GRADE is written on a card and placed in a bag. What is the probability of picking a vowel on t

irga5000 [103]

Answer: Person, I am sorry!

Step-by-step explanation: I Don't know!

4 0

2 years ago

A large diamond with a mass of 712.04 grams was recently discovered in a mine. if the density of the diamond is 3.51 grams over

fredd [130]

Answer:

202.9 cm^3

Step-by-step explanation:

Mass is 712.04 grams

Density is 3.51 grams/cm^3

Volume = (712.04 g)/(3.51 grams/cm^3) = 202.9 cm^3

8 0

1 year ago

637m as a fraction of 7.7km

velikii [3]

Answer:

637/7700

Step-by-step explanation:

7.7 km = 7700 m

3 0

2 years ago