Traffic sign

There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls).

Correct result:

A =  4.004 °
B =  4.014 °

Solution:

r=7%=7100=0.07  tanA=yx=r  A=180πarctan(r)=180πarctan(0.07)=4.004=415"r=7 \%=\dfrac{ 7 }{ 100 }=0.07 \ \\ \ \\ \tan A=\dfrac{ y }{ x }=r \ \\ \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arctan(r)=\dfrac{ 180^\circ }{ \pi } \cdot \arctan(0.07)=4.004 ^\circ =4^\circ 15"
r=y/a a=1 m y1=a r=1 0.07=7100=0.07 m x1=a2y12=120.0720.9975 m  B=180πarctan(y1x1)=180πarctan(0.070.9975)4.014=4.014450"  BAr=y/a \ \\ a=1 \ \text{m} \ \\ y_{1}=a \cdot \ r=1 \cdot \ 0.07=\dfrac{ 7 }{ 100 }=0.07 \ \text{m} \ \\ x_{1}=\sqrt{ a^2-y_{1}^2 }=\sqrt{ 1^2-0.07^2 } \doteq 0.9975 \ \text{m} \ \\ \ \\ B=\dfrac{ 180^\circ }{ \pi } \cdot \arctan(\dfrac{ y_{1} }{ x_{1} } )=\dfrac{ 180^\circ }{ \pi } \cdot \arctan(\dfrac{ 0.07 }{ 0.9975 } ) \doteq 4.014=4.014 ^\circ \doteq 4^\circ 50" \ \\ \ \\ B \approx A



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!


Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Pythagorean theorem is the base for the right triangle calculator.
Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  • Road drop
    atan On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
  • Slope of the pool
    swimming_pool Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 1.13 m (for children) and depth at end is 1.84 m (for swimmers). Slope express as percentage and as angle in degrees.
  • Median
    medians.JPG In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
  • Aircraft
    aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
  • TV tower
    Žižkov_tv_tower Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°?
  • Reference angle
    anglemeter Find the reference angle of each angle:
  • KLM triangle
    trojuholnik_8 Find the length of the sides of the triangle KLM if m = 5cm height to m = 4.5 cm and size MKL angle is 70 degrees.
  • Maple
    tree_javor Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
  • If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  • An observer
    tower An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
  • Depth angles
    hrad At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
  • How far
    lighthouse_1 From the top of a lighthouse 145 ft above sea level, the angle of depression of a boat 29°. How far is the boat from the lighthouse?
  • Profit gain
    percent_12 If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 340, the cost of the article is:
  • Researchers
    house Researchers ask 200 families whether or not they were the homeowner and how many cars they had. Their response was homeowner: 14 no car or one car, two or more cars 86, not homeowner: 38 no car or one car, two or more cars 62. What percent of the families
  • Summerjob
    tree2 The temporary workers planted new trees. Of the total number of 500 seedlings, they managed to plant 426. How many percents did they meet the daily planting limit?
  • Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8