1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
erastova [34]
3 years ago
15

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

rees. The tree stands 20 ft off the hill. How high is the top of the tree from the base of the hill?
Mathematics
1 answer:
julia-pushkina [17]3 years ago
6 0

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.

You might be interested in
Please solve this math problem very simple for points and if your correct you get brainly
____ [38]

Answer:

58 and 1/2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Warren has 40 coins (all nickels, dimes, and quarters) worth $4.05. He has 7 more nickels than dimes. How many quarters does War
alexdok [17]

7 Quarters

20 nickels

13 dimes

5 0
3 years ago
Solve for m.<br><br> -5m = -35<br> m = ?
IgorLugansk [536]
-5m = -35

-5m/-5 = -35/-5

m = 7

Answer: m = 7
6 0
3 years ago
Read 2 more answers
A graph titled velocity versus time has horizontal axis time (seconds) and vertical axis velocity (meters per second). A line ha
AnnyKZ [126]

Acceleration is the change in velocity with respect to the time. The acceleration of the car at segment C is -30 meter per second squared. Hence the option B is the correct option.

<h3>Given information-</h3>

Segment A runs from 0 seconds 0 meters per second to 1 seconds 30 meters per second.

Segment B runs to 3 seconds 30 meters per second.

Segment C runs to 6 seconds 10 meters per second.

Segment D runs to 7 seconds 10 meters per second.

Segment E runs to 10 seconds 20 meters per second.

<h3>Acceleration</h3>

Acceleration is the change in velocity with respect to the time. Acceleration of a vector quantity which means it has both magnitude and the direction. It can be given as,

a=\dfrac{\Delta v}{\Delta t}

Here t denotes the time and v denotes the velocity of the body.

Acceleration at segment C,

a_c=\dfrac{10-40}{6-5}

a_c=-30

Thus the acceleration of the car at segment C is -30 meter per second squared. Hence the option B is the correct option.

Learn more about the acceleration here;

brainly.com/question/2437624

4 0
3 years ago
Read 2 more answers
ITS DUE TODAY HELP PLS Which steps would be used to solve this equation? Check all that apply. Multiply by 3 on both sides of th
kumpel [21]

Answer:

Multiply by 3 on both sides of the equation.

2.78 × 3 = 8.34, so t = 8.34.

Substitute 8.34 for t to check the solution.

Step-by-step explanation:

To solve the equation  = 2.78

we will use the steps below to solve this equation;

First, multiply by 3 on both-side of the equation. That is;

×  3= 2.78 × 3

On the left hand side of the equation 3 will cancel-out 3, leaving us with just t while 3 will be multiply by 2.77 on the right-hand side of the equation to give 8.34

t = 8.34

we can further substitute 8.34 for t to check the correctness of the solution

that is;

=  2.78

R

5 0
3 years ago
Other questions:
  • Can someone please help me with this please?<br> ANSWER ASAP!!!!!!!!!
    13·1 answer
  • Segment lm is the midsegment of trapezoid abcd. ab = 58, and dc = 98. what is lm?
    14·1 answer
  • 17h +1= [3h-7| for h.
    8·1 answer
  • Y" +2y' +17y=0; y(0)=3, y'(0)=17
    15·1 answer
  • Here are two patterns made using identical rhombuses. Without using a protractor, determine the value of a and b.
    8·2 answers
  • I am terrible at math, so i might need some help with this
    7·1 answer
  • HELP PLEASE GIVE THE RIGHT ANSWER.WILL GIVE BRAINLIEST.
    15·1 answer
  • 3x3x3x3x2x2. Complete the expression using exponents
    15·2 answers
  • Which is equal to (2+3i)+(-4+i)?<br> A, -2-4i<br> B, -2-2i<br> C, -2+2i<br> D, -2+4i<br> E, 6+4i
    6·2 answers
  • Please HELP NOW WILL GIVE BRAINLIEST
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!