# Angle + triangle - math 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 - 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? - Trigonometric functions

In right triangle is: ? Determine the value of s and c: ? ? - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - 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. - Observer

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

Triangle KLM is given by plane coordinates of vertices: K[14, -2] L[8, 13] M[-1, -18]. Calculate its area and itsinterior angles. - IS triangle

Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long. - 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°. - Railways

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. - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm. - 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? - 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°? - Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°. - Rotation of the Earth

Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km. - Climb

On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went? - Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.

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