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Trig
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100
Sine function involves which ratio of the sides of the triangle
What is opposite over hypotenuse
100
If I am standing 50 feet from the base of a radio tower and the angle of elevation to the top of the tower is 59 degrees, what is the height of the radio tower?
What is Tan 59 = x/50 x=50*tan 59 83.2 feet
100
What are vector coordinates of 16 mph magnitude and direction of 10 degrees north of east?
What is x=cos10*16 x=15.8 y=sin10*16 y=2.8 Vector coordinates: <15.8, 2.8>
100
Area of a regular pentagon with side length of 6 cm and an apothem of 4.1 cm.
What is Area= .5*4.1*30 Area=61.5 cm squared
100
Which trig function starts very small at 0 degrees and gets very large as the degree measure gets closer to 90 degrees?
What is tangent function?
200
Cosine function involves the ratio of which two sides of the triangle
What is adjacent over hypotenuse
200
The guy wire from the ground to the top of the radio tower is 92 feet long and the angle of elevation from the ground is 73 degrees. At what height does the guy wire attach to the tower?
What is Sin 73=x/92 x=92*sin 73 88.0 feet
200
What are the coordinates for a 24 mph vector at 15 degrees north of west?
What is sin15=y/24 y=24*sin15=6.2 cos 15=x/24 x=24*cos15=23.2 <-23.2, 6.2>
200
Area of a decagon with an apothem of 10 in
What is Side length: tan 18=x/10 x=10*tan 18 so full side length is 6.498 Area =.5*10*(10*6.498) 324.9 in squared
200
If you were in a blimp and you need to find out the length of your line-of-sight and the blimp's altitude is 400 feet and the angle of depression is 20 degrees?
What is Cos 70 = 400/x 400=x*cos 70 400/cos70=x x=1169.5 feet or sin 20 = 400/x 400 = x*sin 20 400/sin 20 = x x=1169.5 feet
300
Tangent function involves the ratio of which two sides of the triangle
What is opposite over adjacent?
300
A man is using a 5 foot transit. He sees a 51 degree angle of elevation to the top of the building. The man is standing 40 feet from the base of the building. How tall is the building?
What is Tangent 51=x/40 x=40*tan 51 x=49.4 feet but transit is 5 feet tall so total height of building is 54.4 feet.
300
If a plane is traveling 250 mph heading due south and it runs into a east wind at 35 mph, what is the resulting speed and direction?
What is Direction tanx=35/250 tan inverse(35/250)=x x=8.1 degrees east of south or 81.9 south of east magnitude: 352 + 2502=m2 magnitude: 252.4 mph
300
Area of a regular octagon with a radius of 20 inches
What is Angle in “large” triangle is 45 so the angle becomes 22.5 when I draw in the apothem. Apothem: cos22.5=a/20 a=18.47759 Side length: sin22.5 = x/20 x=7.654 side length is 2*7.654=15.307 Area=.5*18.47759*(8*15.307) Area=1131.3 inches squared
300
Prove that tan x= sin x/cos x using the definitions of those functions. Use this triangle's side lengths: a and b are legs while c is the hypotenuse. x is the angle between c and b.
What is sinx/cosx = a/c over b/c =a/c * c/b = a/b which is tan x
400
When finding the area of a triangle using SAS, what function do we always use?
What is sine function?
400
A man is on the top of a building and he is looking down at a 20 degree angle of depression. He knows his building is 150 feet tall and the shorter building is 50 feet away. How tall is the shorter building?
What is Tan 70 = 50/x 50=x*tan 70 50/tan 70 = x c=18.2 feet so height of building is 150 – 18.2= 131.8 feet
400
A UPS van travels 180 miles to the east. It then travels 45 miles to the south. How many miles (as the crow flies) back to its starting point and what direction will it need to travel to get back to its starting point?
What is Magnitude: 1802 + 452= m2 Magnitude: 185.5 miles Direction back to starting point: tan inverse (180/45)= 76.0 degrees east of north or 14.0 degrees north of east
400
Area of triangle with side lengths of 19 cm, 10 cm, and the angle of 35 degrees between those two sides
What is Area= .5*10*19*sin35 Area=54.5 cm squared Height=sin 35=h/19
400
Prove: (sin x)^2 + (cos x)^2 = 1 use the definitions of these functions.
What is opp^2/hyp^2 + adj^2/hyp^2 =(opp^2 + adj^2)/hyp^2 =hyp^2/hyp^2 =1
500
A lady is lying 40 feet from the base of a tree and the tree is 70 feet tall. What is the angle of elevation from the lady to the top of the tree?
What is Tan x = 70/40 tan inverse of 70/40 = x x = 60.3 degrees
500
A van travels 27 miles at 13 degrees west of south and then it travels 179 miles 42 degrees west of north. What is the resultant of these two vectors?
What is First vector: sin13 = x/27 x= -6.1 cos13 = y/27 y= -26.3 Second vector: sin42=x/179 x= -119.8 cos42 = y/179 y=133.0 Resultant: < -125.9, 106.7>
500
Area of triangle of 26 in, 34 in, and an angle of 54 degrees between those two sides?
What is Area=.5*34*26*sin54 Height of triangle sin54=x/26
500
Prove that sinx = tanx * cosx
What is tanx* cosx = (opp/adj)*(adj/ hyp) = opp/hyp =sin x