Angle - math word problems
- Depth angles
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
An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
- The second
The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
- Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
How many times a day hands on a clock overlap?
- Is right?
Is triangle with sides 51, 56 and 77 right triangle?
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
- It is rectangular?
Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
Triangle KLM is given by plane coordinates of vertices: K[14, -2] L[8, 13] M[-1, -18]. Calculate its area and itsinterior angles.
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
- IS triangle
Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
- Slope of track
Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long.
- Climb in percentage
The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.