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
Anika [276]
3 years ago
9

To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level) b = 800 meters fro

m the base of the mountain to the top of the mountain is β = 59 ∘ . The students then walk a = 2550 meters straight back and measure the angle of elevation to now be α = 32 ∘ . If we assume that the ground is level, use this information to estimate the height of the mountain.
Mathematics
2 answers:
In-s [12.5K]3 years ago
8 0

Answer:

1462 m

Step-by-step explanation:

Given:-

- The height of the mountain = h

- The distance from the base of mountain to first position, b = 800 m

- The angle of elevation of top of mountain from 1st position, β = 59°

- The amount of distance walked away from initial position, a = 2550 m

- The new angle of elevation of top of mountain, α = 32°

Find:-

If we assume that the ground is level, use this information to estimate the height of the mountain.

Solution:-

- We will sketch two triangles. First triangle would have a vertical height " h " that will denote the height of the mountain. Then a horizontal line " b " which is the initial position from the base of the mountain. The connect the ends of vertical and horizontal line by an hypotenuse. Forming and angle of elevation from first position to be β .

- Then we will use the trigonometric function of tangent to determine the height "h":

                             tan ( β ) = h1 / b

                             h1 = b*tan ( β )

                             h1 = 800*tan ( 59 )

                             h1 = 1331.42358 m

- Similarly, second triangle would have a vertical height " h " that will denote the height of the mountain. Then a horizontal line " a " which is the final position from the base of the mountain. The connect the ends of vertical and horizontal line by an hypotenuse. Forming and angle of elevation from final position to be α .

- Then we will use the trigonometric function of tangent to determine the height "h":

                             tan ( α ) = h2 / ( a )

                             h2 = (a)*tan ( β )

                             h2 = (2550)*tan ( 32 )

                             h2 = 1593.416 m

- To estimate the height of the mountain we will take an average of the two values obtained:

                            h_avg = ( h1 + h2 ) / 2

                                       = ( 1331.42358 + 1593.416 ) / 2

                                       = 1462.41979 m

Nady [450]3 years ago
6 0

Answer: The height of the mountain is 1,331.4 meters (approximately)

Step-by-step explanation: From the information given, the students were standing at point b which is 800 meters from the base of the mountain and the angle of elevation from that point is 59°. Assuming that the ground is level, we can derive a right angled triangle from this set of details and hence we have triangle ABC, where angle β is the reference angle, (59 degrees), BC is the distance from the students to the base of the mountain (800 meters) and the line AC is the height of the mountain.

The line AC is the opposite, since angle B is the reference angle, therefore we shall use the trigonometric ratio as follows;

Tan β = opposite/adjacent

Tan 59 = AC/800

Tan 59 x 800 = AC

1.6643 x 800 = AC

1331.44 = AC

AC ≈ 1331.4

Therefore the height of the mountain is approximately 1,331.4 meters

You might be interested in
(05.05 HC) Figure ABCD has vertices A(-3, 2), B(2, 2), C(2, -4), and D(-3, -2). What is the area of Figure ABCD?​
irga5000 [103]

Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

.

6 0
2 years ago
A number is divided by four. The result is divided by
Vikentia [17]
The original number is 24
2 x 3 = 6
6 x 4 = 24 
or 
24 / 4 = 6 
6 / 3 = 2
4 0
3 years ago
Read 2 more answers
The probability for success of an event is P(A), and the probability of success of a second, independent event is P(B). What is
Alborosie

Given:

The probability for success of an event is P(A)

The probability of success of a second, independent event is P(B).

To find:

The probability of both events occurring, in that order.

Solution:

If A and B are two independent events, then

P(A\cap B)=P(A)\cdot P(B)

It is given that,

The probability for success of an event is P(A)

The probability of success of a second, independent event is P(B).

Since A and B both are independent event and we need to find the probability of both events occurring, in that order, i.e., P(A\cap B), therefore P(A\cap B)=P(A)\cdot P(B).

Hence, the correct option is A.

5 0
3 years ago
How do you know that two expressions are equivalent
stiks02 [169]
You know that two expressions are equivalent when if you substitute in your values and simply the expressions, they have the same answer.
6 0
3 years ago
Why is this wrong?<br> What is the rigth answer?
pantera1 [17]
For every 7 votes for candidate a, there are 4 votes for candidate c
3 0
3 years ago
Other questions:
  • Samantha bought 4/9 pounds of sunflower seeds, Brittany bought 0.4 pound and Tia bought 44/100 pound. List the numbers in order
    15·1 answer
  • This​ week, 951 people went to the beach. Last​ week, 1 comma 221 people went to the beach. The number of people who went to the
    7·1 answer
  • What change do you have to make to the graph of f (x) = 7x in order to graph the function g (x) = 7x+10?
    14·1 answer
  • Shania's test scores in 8 subjects were 88, 91, 85, 74, 69, 72, 80, and 87. Shania found the middle number of her scores. Which
    15·2 answers
  • The price of a stock is $3.17 per share. what is the greatest number of whole shares mr. smith can buy with $200?
    10·2 answers
  • PLEASE HELP, WILL MARK BRAINLIEST
    13·1 answer
  • A triangle and a parallelogram have the same base and the same area.
    14·1 answer
  • Evaluate 5-\dfrac{t}35−
    5·2 answers
  • Rea Calculations
    11·1 answer
  • What is the meaning of the point with an x coordinate of 2 ​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!