# Angle + triangle - examples

1. Lighthouse
Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea.
2. Find the 9
Find the missing angle in the triangle and then name triangle. Angles are: 95, 2x+15, x+3
3. Isosceles triangle 8
If the rate of the sides an isosceles triangle is 7:6:7, find the base angle correct to the nearest degree.
4. Cable car
Find the elevation difference of the cable car when it rises by 67 per mille and the rope length is 930 m.
5. Trigonometric functions
In right triangle is: ? Determine the value of s and c: ? ?
6. Is right?
Is triangle with sides 51, 56 and 77 right triangle?
7. River
From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
8. 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?
9. It is rectangular?
Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
10. Triangle
Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles.
11. IS triangle
Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
12. 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°.
13. Railways
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
14. Slope of track
Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Topoľčany (174 m AMSL), if the track is 44 km long.
15. Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
16. Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
17. 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?
18. 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°?
19. Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
20. 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.

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