Angle + right triangle - math problems

1. 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
2. River Calculate how many promiles river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL.
3. Trigonometric functions In right triangle is: ? Determine the value of s and c: ? ?
4. Is right? Is triangle with sides 51, 56 and 77 right triangle?
5. 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.
6. River 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.
7. It is rectangular? Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
8. Right Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
9. IS triangle Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
10. 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.
11. Cone 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°.
12. Railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
13. 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.
14. 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.
15. Mast Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'.
16. Rectangle Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
17. Isosceles right triangle Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
18. Circular pool The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
19. Similarity Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
20. Diagonal Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.