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The question is incomplete. The map is attached as a photo and here is the complete question:
a. What is the actual distance between Saugerties and
Kingston? ___________________________
b. Catskill is 15 miles from Saugerties. What would the
distance on the map be? ___________________________
c. On another map, the distance between Saugerties and
Kingston is 2 inches. What would the distance from Saugerties to
Catskill be on this map? __________________
Since you have asked the answer for part (c) only, here is the answer:
Answer:
<u>The distance from Saugerties to Catskill would be </u><u>3 inches</u><u> on this map.</u>
Step-by-step explanation:
On the given map, the distance between Saugerties and Kingston is 4 inches and the scale is <u>1 inch = 2.5 miles.</u>
To calculate the actual distance in miles between Saugerties and Kingston, consider the given scale:
1 inch ---------- 2.5 miles
4 inches ------ x miles
Cross multiplying:
1x = 2.5 x 4
x = 10 miles
The actual distance between Saugerties and Kingston is 10 miles.
On another map, the distance between Saugerties and Kingston is 2 inches. Which means the scale is 2 inches = 10 miles. So 1 inch = 10/2 = 5 miles
The scale on the other map is 1 inch = 5 miles.
Catskill is 15 miles from Saugerties (given in the previous part). So on the map:
1 inch -------- 5 miles
y inch ------- 15 miles
Cross multiplying:
15 = 5y
y = 15/5
<u>y = 3 inches.</u>
The distance from Saugerties to Catskill would be 3 inches on this map.
The given point (-3/5 , y) lies in the third quadrant.
It is also given that the point lies on a unit circle.
For a point (x,y) lying on a unit circle a and y are defined as:
x = cos θ
y = sin θ
So, we can say for the point (-3/5 , y) the value -3/5 is equal to cos θ
sec θ is the reciprocal of cos θ.
So, sec θ = -5/3
Using Pythagorean identity we can first find sin θ.
Since the point lies in 3rd quadrant, both sin and cos will be negative.
So, now we can write:
Answers:
sec θ = -5/3
cot θ = 3/4
It is also given that the point lies on a unit circle.
For a point (x,y) lying on a unit circle a and y are defined as:
x = cos θ
y = sin θ
So, we can say for the point (-3/5 , y) the value -3/5 is equal to cos θ
sec θ is the reciprocal of cos θ.
So, sec θ = -5/3
Using Pythagorean identity we can first find sin θ.
Since the point lies in 3rd quadrant, both sin and cos will be negative.
So, now we can write:
Answers:
sec θ = -5/3
cot θ = 3/4