Mathematics, 20.02.2020 05:37 dianereyes7475

B. Tom and Sam are on the opposite sides of a building (they are outside the building) of 160 meters

height. They measure the angle of elevation of the top of the tower as 40° and 55° respectively. If the

building is 50 meters wide, find the distance between Tom and Sam.

Answers: 1

Show answers

Answers

Answer from: Jorjalilli8081

The distance between Tom and Sam is about 352.37m.

Step-by-step explanation:

Previous explanation

We can answer this question using Trigonometry.

Firstly, we need to draw all the information given in the question:

Tom and Sam are on the opposite sides of a building and outside it.The building's height is 160 meters.The angles of elevation are measured from the positions Tom and Sam are. They are 40 and 55 degrees, respectively. We can see if we draw a line from Tom's position to the top of the building, we can form a triangle, as depicted in the graph below. The same applies to Sam's position (that is, we can form another triangle).The building is 50 meters wide, which completes the needed information to solve the question.

We attached a graph containing all this information (see below).

Solution

Having the elevation angles, the building height and width, from graph below, we can determine that the total distance is:

$\\ d_{T} = d_{Tom} + 50m + d_{Sam}$

Where

$\\ d_{Tom}\;is\;the\;Tom's\;distance\;from\;the\;building$ .

$\\ d_{Sam}\;is\;the\;Sam's\;distance\;from\;the\;building$ .

Knowing from Trigonometry that the tangent of an angle is defined as:

$\\ tan(\theta) = \frac{opposite\;side\;of\;\theta}{adjacent\;side\;of\;\theta}$

Then

$\\ tan(\alpha) = \frac{opposite\;side\;of\;\alpha}{adjacent\;side\;of\;\alpha}$

And

$\\ tan(\beta) = \frac{opposite\;side\;of\;\beta}{adjacent\;side\;of\;\beta}$

The opposite side of $\\ \alpha$ is the height of the building (160m). The same is the case for the opposite side of $\\ \beta$ , that is, the height of the building too.

The adjacent side for $\\ \alpha$ is $\\ d_{Tom}$ and for $\\ \beta$ is $\\ d_{Sam}$ .

The value of the tangent for an angle (alpha, in this case) = 40 degrees, rounding it to two decimals places is about: tan(40) = 0.84.

The value of the tangent for an angle (beta, in this case)= 55 degrees, rounding it to two decimals places is approximately: tan(55) = 1.43.

Then

$\\ tan(\alpha) = \frac{160m}{d_{Tom}}$

Solving the equation for the distance from Tom to the building:

$\\ tan(\alpha) = \frac{160m}{d_{Tom}}$

$\\ d_{Tom} = \frac{160m}{tan(40)}$

$\\ d_{Tom} = \frac{160m}{0.84}$

$\\ d_{Tom} = \frac{160m}{0.84} \approx 190.48m$

For calculating Sam's distance from the building, we can proceed following the same steps:

$\\ tan(\beta) = \frac{160m}{d_{Sam}}$

$\\ d_{Sam} = \frac{160m}{tan(\beta)}$

$\\ d_{Sam} = \frac{160m}{1.43} \approx 111.89m$

The distance between Tom and Sam is the resulting value of the sums:

$\\ d_{T} = d_{Tom} + 50m + d_{Sam}$

$\\ d_{T} = 190.48m + 50m + 111.89m$

$\\ d_{T} = 352.37m$

Thus, The distance between Tom and Sam is about 352.37m.

See the graph below.

(Note: without rounding the respectives values for tangent of each angle, the value for the distance is about 352.71m).

B. Tom and Sam are on the opposite sides of a building (they are outside the building) of 160 meters

Answer from: Quest

that one look

step-by-step explanation:

Answer from: Quest

answer: the correct option is d.

explanation:

it is given that the triangle j'k'l' shown on the grid below is a dilation of triangle jkl using the origin as the center of dilation.

from the given graph it is noticed that k(4,8) and k'(2,4). let origin is defined by o and scale factor is defined by k, then

$k=\frac{ok'}{ok}$ (1)

distance formula,

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$ok'=\sqrt{(2-0)^2+(4-0)^2}= \sqrt{4+16}= \sqrt{20}=2\sqrt{5}$

$ok=\sqrt{(4-0)^2+(8-0)^2}= \sqrt{16+64}= \sqrt{80}=4\sqrt{5}$

put these values in equation (1).

$k=\frac{2\sqrt{5}}{4\sqrt{5}}= \frac{1}{2}$

therefore scale factor is $\frac{1}{2}$ and option d is correct.

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More questions: Mathematics Another questions

B. Tom and Sam are on the opposite sides of a building (they are outside the building) of 160 meters height. They measure the angle of elevation of the top of the tower as 40° and 55° respectively. If the building is 50 meters wide, find the distance between Tom and Sam.

Answers

Another question on Mathematics

B. Tom and Sam are on the opposite sides of a building (they are outside the building) of 160 meters

height. They measure the angle of elevation of the top of the tower as 40° and 55° respectively. If the

building is 50 meters wide, find the distance between Tom and Sam.