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
ale4655 [162]
3 years ago
5

Tara wants to fix the location of a mountain by taking measurements from two positions 3 miles apart. From the first position, t

he angle between the mountain and the second position is 78o. From the second position, the angle between the mountain and the first position is 53o. Find the SHORTEST distance to the mountain. Round to the nearest hundredth of a mile (two decimal places).
Mathematics
1 answer:
Black_prince [1.1K]3 years ago
7 0

Answer:

Shortest distance from the mountain is 3.17 miles.

Step-by-step explanation:

From the figure attached,

Let a mountain is located at point A.

Angle between the mountain and point B (∠B) = 53°

Angle between the mountain and point C (∠C) = 78°

Distance between these points = 3 miles

Since, m∠A + m∠B + m∠C = 180°

m∠A + 53° + 78° = 180°

m∠A = 180°- 131° = 49°

By applying sine rule in triangle ABC,

\frac{\text{sin}(49)}{BC}=\frac{\text{sin}(53)}{AC}= \frac{\text{sin}(78)}{AB}

\frac{\text{sin}(49)}{3}=\frac{\text{sin}(53)}{AC}= \frac{\text{sin}(78)}{AB}

\frac{\text{sin}(49)}{3}=\frac{\text{sin}(53)}{AC}

AC = \frac{3\text{sin}(53)}{\text{sin}(49)}

AC = 3.17 miles

\frac{\text{sin}(49)}{3}=\frac{\text{sin}(78)}{AB}

AB = \frac{3\text{sin}(78)}{\text{sin}(49)}

AB = 3.89 miles

Therefore, shortest distance from the mountain is 3.17 miles.

You might be interested in
Alina is able to swim at a rate of about 2.5 miles per hour. Talia is able to swim at a rate of 1.8 meters per second. Which sta
kirza4 [7]

Remark

Without being given choices, we can get answers but they may not be listed among your. The important think is to be working in the same units

Convert miles/hour to m/sec

\frac{2.5 mi}{h}*\frac{1 h}{3600 sec}*\frac{1.6 km}{1 mi}*\frac{1000 m}{1 km}

Now just multiply all the numerators together and divide by all the denominators.

<em><u>Numerators:</u></em> 2.5 * 1.6 * 1000 = 4000

<em><u>Denominators:</u></em> 3600

numerator/denominator = 4000/3600 m/s = 1.111 m/s

Conclusion

Talia is a much faster swimmer than Alina because 1.8 is greater than 1.11. Both numbers are in m/s.

2.5 miles / hour = 1.


5 0
3 years ago
Read 2 more answers
The volume of the cone is 130 units^3. Solve for x.<br> Height: 13<br> Radius: x
Gwar [14]
V=(1/3)hpir^2
v=130
h=13
r=x

130=(1/3)(13)pix^2
times both sides by 3
390=13pix^2
divide both sides by 13
30=pix^2
divide both sides by pi
30/pi=x^2
sqrt both sides
x≈3.09
radius is abou 3 units
3 0
3 years ago
List all the points that are on the same plane as point V
topjm [15]
I believe the points should be as follows : X, S, Y, and U.
3 0
2 years ago
Two submarines are underwater. The number -4,845 represents Submarine A's position (in feet) relative to the surface. The number
kolbaska11 [484]

Answer

a

Step-by-step explanation:

because submarine b has a bigger negative number so its more further down

6 0
3 years ago
Moscow, the capital city of Russia, is at 37.62 degrees longitude and 55.75 degrees latitude. Brasilia, the capital city of Braz
Vsevolod [243]

Answer:

drfcexdw

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • Why is a ray a defined term
    7·1 answer
  • A rectangular auditorium seats 1702 people. The number of seats in each row exceeds the number of rows by 9. Find the number of
    12·1 answer
  • SA is the perpendicular bisector of TR. m∠TSR=120 Which other statement is true?
    10·2 answers
  • Scientist cindy Grade has developed a new thermometer. Unlike the thermometer developed by Gabriel Fahrenheit were 32°F marks th
    9·1 answer
  • Help me pls, question for smart people
    6·2 answers
  • A potato gun is a device made out of plastic pipe that launches a potato using compressed air. They can be great fun, and even e
    9·1 answer
  • What is the value of 3 in 9.237
    8·2 answers
  • HELPP plz I need the answer with step by step don't send a file plz
    11·1 answer
  • Simplify the expression. 3.6 - 3.1n -2n + 5
    7·2 answers
  • Pauline rides his bike to school in 6 2/5 minutes. If it takes Dylan 4 1/2 times as long to get to school, how long would it tak
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!