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3 years ago

The scale of a map is 1 cm: 12 km. Find the actual distance for 1.5 cm

Mathematics

2 answers:

Lina20 [59]3 years ago

8 0

The answer for 1.5 km is 18

WARRIOR [948]3 years ago

3 0

1cm=12km
1.5cm=?mk
The answer is 18, I quickly did this one in my head by finding half of 12 and adding it with 12, but the mathematical way to do it is to multiply 1.5 by 12.

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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

Two friends, Hailey and Jenna bought two tickets to see a play at a local theater . Each ticket cost $17.25. Each friend donated

Sliva [168]

Per ticket cost $17.25

Per person conveyance fee $3.00

Percent increase in the cost of per ticket

17.39%

8 0

3 years ago

What is the difference of the fractions? Use the number line and equivalent fractions to help find the answer.

Dmitry_Shevchenko [17]

9514 1404 393

Answer:

Step-by-step explanation:

Subtracting a positive number moves you to the left on the number line. Subtracting a negative number moves you in the opposite direction, to the right.

Here, we start at -2 1/2 = -5/2, and we move 1 3/4 = 7/4 to the right from there. Each mark on this number line is 1/4 unit, so we move 7 marks. The results is ...

-2 1/2 -(-1 3/4) = -5/2 +7/4

= -10/4 +7/4 = -3/4

5 0

3 years ago

My question is in the attachment.<br>

Nikolay [14]

Answer:

5 and 25

Step-by-step explanation:

let the son's age be x then the father's age is x + 20

In 5 years

son = x + 5 and father = x + 20 + 5 = x + 25

Then

x + 25 = 3(x + 5) ← father is three times as old as son

x + 25 = 3x + 15 ( subtract x from both sides )

25 = 2x + 15 ( subtract 15 from both sides )

10 = 2x ( divide both sides by 2 )

5 = x and x + 20 = 5 + 20 = 25

si=on is 5 and father is 25

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Find the value of x in the triangle shown below

Sonbull [250]

Answer:

nice

Step-by-step explanation:

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3 years ago

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