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
Papessa [141]
3 years ago
5

A chimpanzee sitting against his favorite tree gets up and walks 70.9 m due east and 31.9 m due south to reach a termite mound,

where he eats lunch. (a) What is the shortest distance between the tree and the termite mound? (b) What direction does the shortest distance make, as a positive angle with respect to due east?
Physics
1 answer:
DIA [1.3K]3 years ago
4 0
A right triangle is formed by the 70.9 m walked east and 31.9 m walked south.
The legs of this right triangle are 70.9 and 31.9.
The shortest distance between two points is a straaight line. Therefore the hypotenuse of this triangle is going to be that shortest distance.
We can use the Pythagorean Theorem to find the hypotenuse of this triangle.
a^2+b^2=c^2\\70.9^2+31.9^2=c^2\\5026.81+1017.61=c^2\\6044.42=c^2\\c=\sqrt{6044.42}

c=\sqrt{6044.42}\approx\boxed{77.7458681}\ (decimal\ form)\\\\c=\sqrt{6044.42}=\sqrt{\frac{604442}{100}}=\boxed{\frac{\sqrt{604442}}{10}}\ (exact\ form)

As for the second part of the question, we want to find the angle formed by the hypotenuse and the 31.9 walked east.
We could use any of the three trigonometric ratios here since we know all 3 sides.
sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangent = opposite / adjacent
I am going to use tangent, because then I won't have to deal with the hypotenuse and so the answer will be more accurate.

If you haven't already drawn yourself a diagram, now is a good time to.
The side opposite our angle is the 31.9, and the adjacent is 70.9.
Therefore, \tan(m\angle)=\frac{31.9}{70.9}.

We can use inverse trig ratios here to find the measure of our angle.
\tan^{-1}(\tan(m\angle))=\tan^{-1}(\frac{31.9}{70.9})\\\\m\angle=\tan^{-1}(\frac{31.9}{70.9})\approx\boxed{24.2243851\°\ or\ 0.422795279\ rad}
You might be interested in
3 track athletes run the 400 meter dash, Jackie 51 seconds and 1500 joules
Aleksandr [31]

Answer:

ish all usual isaiah or easier fall iF.Hg. diff potty off radial ish usually appraisal

7 0
2 years ago
A living thing that feeds on Another living thing and may kill it eventually is called
Murljashka [212]

Answer:

(D) parasite........................

3 0
2 years ago
I’ll mark you as brinlist please help.
Ede4ka [16]

Answer:

245 divided by 5.14=47.6653696 or 47.66

Explanation:

8 0
3 years ago
Read 2 more answers
Please help me!
Kay [80]
Runoff because the mud is a liquid and moves on an amount of water that is in it like with quicksand
5 0
3 years ago
Read 2 more answers
A star with a large luminosity would have a relatively _____ absolute magnitude.
Mademuasel [1]
A star with large luminosity would have a relatively low absolute magnitude. Absolute magnitude is a number that tells how bright a star is from the Earth. However, this scale is backwards and logarithmic, so having a large absolute magnitude value means that the star is faint.
3 0
2 years ago
Other questions:
  • A motor vehicle has a mass of 1.8 tonnes and its wheelbase is 3 m. The centre of gravity of the vehicle is situated in the centr
    14·1 answer
  • On the Moon, the acceleration due to the effect of gravity is only about 1/6 of that on Earth. An astronaut whose weight on Eart
    15·2 answers
  • CAN SOMEONE HELP PLEASE
    8·1 answer
  • A hockey player makes a slap shot exerting a constant force of 40.0 newtons on the puck for .2 seconds. What is the magnitude of
    10·1 answer
  • Bandwidth is the: Select one: A. number of frequencies that can be broadcast through a medium. B. number of cycles per second th
    8·1 answer
  • An object will have the same mass and weight on the moon as it has on Earth.
    7·1 answer
  • Oxygenated hemoglobin absorbs weakly in the red (hence its red color) and strongly in the near infrared, whereas deoxygenated he
    10·1 answer
  • Determine the Reynolds number for a flow of 0.2 m^3/s through a 203 mm inner diameter circular pipe of a fluid with rho=680 kg/m
    8·1 answer
  • A sample of hydrogen at 1.5 atm had its pressure decreased to 0.50 atm producing a new volume of 750 mL. What was its original v
    10·1 answer
  • When you do glass blowing is it a chemical change or a physical change
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!