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3 years ago

What is the radius of a circle if its area is 120 in2? (Round your answer to the nearest hundredth of an inch)

Mathematics

1 answer:

asambeis [7]3 years ago

8 0

Answer:

6.18

Step-by-step explanation:

120/3.14, square root then round

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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

What is the trinomial factor of x^3 + y^3 ?

sammy [17]

Answer:

Step-by-step explanation:

x³ + y³ ← is a sum of cubes and factors in general as

x³ + y³ = (x + y)(x² - xy + y²)

with trinomial factor (x2 - xy + y2) → B

3 0

3 years ago

Are the triangles congruent? if they are, state how they are congruent.

Juliette [100K]

Answer: Yes

Step-by-step explanation: by SAS

8 0

3 years ago

Read 2 more answers

Find the volume of the cylinder please help show work

Alinara [238K]

3.
$v = \pi {r}^{2} h$
the volume equation for cylinder
$v = \pi {6}^{2} (12) \\ v = \pi36(12) \\ v = 432\pi \\ v = 1357.16$
5. diameter =half of radius
$v = \pi { 27.2}^{2} (15) \\ v = \pi295.24(15) \\ v = 4437.6\pi \\ v = 13941.13$

4 0

4 years ago

Plz help me do these please its hard and I don't get it

Scrat [10]

Answer:

Step-by-step explanation:

2/10: 0.2

19/20: 0.95

19/6: 3.1667

17/4: 4.25

7/4: 1.75

9/20: 0.45

4 0

3 years ago