Angle - 9th grade (14y) - examples
- Isosceles right triangle
Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
Railways climb 5.8 ‰. Calculate the height difference between two points on the railway distant 2389 meters.
- Angles and sides of the triangle
Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
Calculate how many promiles river Hudson average falls, if on section long 921 km flowing water from 1224 m AMSL to 154 m AMSL.
How many times a day hands on a clock overlap?
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
- Climb in percentage
The height difference between points A and B is 442 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 6.8 km.
- Road - permille
5 km long road begins at an altitude 500 meters above sea level and ends at a altitude 521 ASL. How many permille road rises?
- Mountain railway
Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
The longer leg of a 30°-60°-90° triangle measures 7. What is the length of the shorter leg?
What angle are between directions W (West) and SE (SouthEast) on the compass?
The point (21, 20) is on the terminal side of angle θ. cos θ = ?
- Diagonal in rectangle
In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
- Cable car 2
Cable car rises at an angle 39° and connects the upper and lower station with an altitude difference of 345 m. How long is the track of cable car?
Convert 54° to radians. Write result as multiple of number π.
- Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
For horizontal distance 3 km road rise by 5.4 m. Calculate the road pitch in ‰ (permille, parts per thousand).
- Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=69°. What sizes have other angles in a triangle?
- Radians compare
What is greater angle? 1 radians or 1π radians?