While playing a scavenger hunt game, anthony walks 48.0 m to the south and then walks 12.0 m to the west. what single straight-line displacement could anthony have taken to reach this point? (use trigonometry to answer, but remember to draw a diagram to your understanding.) give both the magnitude and the angle in your answer.

answer options
-49.5 m and 14° west of south
-60.0 m and 76° west of south
-49.5 m and 14° southwest
-49.5 m and 12° southwest

-49.5 m and 14° southwest

Explanation:

In order to solve this you first have to remember the rules of trigonometry, so you know that in any right triangle the summ of its squared sides it´s equal to the hypotenuse squared. So we first calculate the magnitude of the hypotenuse:

The adjacent would be the Y vector, it´s important to knoe where is the location of our angle to be able to properly calculate its dimensions later, and the opposite will be the X vector:

Now we know that the vector is 49.5 rounded.

To calculate the angle we just have trigonometry, and as we know the value of all the sides we can use inverse sine of opp/hyp:

Inverse sine=14.04º

So since the angle that we chose is departing from the Y axis, and into the left of the graph, we now that it is south, and west, so the magnitude is -49.5 m 14º south west.

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this