Question 1. part 1: use the trigonometric ratios sine, cosine, and tangent to answer the following questions. find the sine, cosine, and tangent ratios of angle x.
part 2: use the trigonometric ratios sine, cosine, and tangent to answer the following questions. find the sine, cosine, and tangent ratios of angle y.

question 2. a ski resort is building a new ski lift that will transport tourists from the base of the mountain to its highest point. this mountain has a vertical height of 200 yards, and the ski lift will rise at an angle of 40 degrees. when the project is completed, how many yards, d, will a tourist travel from the base of the mountain to its peak?

part i: sketch a figure to illustrate the scenario above. label the vertices and the lengths that are given in the question.

part ii: using your sketch from part i, write an equation using a trigonometric ratio to find the distance a tourist will travel from the base of the mountain to its peak. round your answer to the nearest 100th. show your work.

1.sin x = \frac{5}{13}

cos x = \frac{12}{13}

tan x = \frac{5}{12}

sin y = \frac{12}{13}

cos y = \frac{5}{13}

tan y = \frac{12}{5}

2. ditance travelled = hypotenuse = \frac{200}{sin 40} = 311.14yards

Step-by-step explanation:

sin x =

cos x =  

tan x =  

therefore from the figure sin x = \frac{5}{13}

cos x = \frac{12}{13}

tan x = \frac{5}{12}

according to angle y height will be 12 and base will be 5

therefore sin y = \frac{12}{13}

cos y = \frac{5}{13}

tan y = \frac{12}{5}

2. given that height = 200 yards and angle x= 40

we know that tan x = \frac{height}{base}

therefore tan 40 = \frac{200}{base}

therefore base = \frac{200}{tan 40}

they have asked us to find hypotenuse therefore

sin x = \frac{height}{hypotenuse}

hypotenuse = \frac{200}{sin 40} = 311.14yards

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

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step-by-step explanation: