# Goniometry and trigonometry - practice problems - page 2 of 28

#### Number of problems found: 546

- Carousel for children

There are 5 seats evenly distributed on the children's carousel in the shape of a circle. What kind the arm of the carousel (connecting the center of the carousel to the seat) is long if the distance between with two seats is 1.2m? - Seats on carousel

There are 12 seats evenly distributed on the children's carousel in the shape of a circle. How long is the arm of the carousel (connecting the center of the carousel to the seat) if the distance between the two seats is 1.5m? - Observer's 82805

An airliner currently flying over a location 2,400 m away from the observer's location is seen at an elevation angle of 26° 20'. At what height does the plane fly? - A chord

In a circle radius of 6 cm, a chord is drawn 3 cm from the center. Calculate the angle subtended by the cord at the center of the circle Hence find the length of the minor arc cut off by the chord. - Bridge across the river

The width of the river is 89 m. For terrain reasons, the bridge deviates from a common perpendicular to both banks by an angle of 12° 30 '. Calculate how many meters the bridge is longer than the river. - Steps

Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º, and the step length is 28.6 cm. Report the result in centimeters to the nearest centimeter. - Elevation angles

Two endpoints distant 240 m are inclined at an angle of 18°15'. The top of the mountain can be seen at elevation angles of 43° and 51° from its. How high is the mountain? - Components 2565

The component is a regular decagon with a side of 2 cm. Its material weight of 1 m² of sheet metal is 24 kg. What is the weight of 200 components? - Aircraft

The plane flies at altitude 6300 m. At the time of the first measurement was to see the elevation angle of 21° and the second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements. - Reflector

The circular reflector throws a light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane? - Observation 76644

From the smaller observation tower, we see the top of the larger tower at an elevation angle of 23°, and the difference in their heights is 12 m. How far apart are the observation towers? - Horizontal 66434

The lower station of the cable car in Smokovec is at an altitude of 1025m, and the upper station at Hrebienk is at an altitude of 1272m. Calculate the climb of the cable car if the horizontal distance between the slopes is 1921m. - Maggie

Maggie observes a car and a tree from a window. The angle of depression of the car is 45 degrees, and that of the tree is 30 degrees. If the distance between the vehicle and the tree is 100 m, find Maggie's distance from the tree. - The mast

A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Elevation 80866

Find the height of the tower when the geodetic measured two angles of elevation α=34° 30'' and β=41°. The distance between places AB is 14 meters. - Diagonals 5113

In the diamond KLMN, the lengths of the diagonals are 10 cm and 6 cm. Determine the angle size that the longer diagonal makes with the side of the diamond. - Difference 81888

The ropeway climbs at an angle of 22°30'. Calculate its length if the height difference between the lower and upper station is 560m. Sketch a picture - SAS triangle

The triangle has two sides, long 7 and 19, and makes included angle 110°42'. Calculate the area of this triangle. - Tourist 39691

How far from the lookout tower, 48 m high, did the tourist stand if he saw its top at an angle of 40 °? - Vertically 82162

The pole is stuck vertically into the ground. The protruding length is 1m. What is the length of the shadow cast when the sun is just 50° above the horizon?

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