Goniometry and trigonometry - practice problems - page 4 of 32
Number of problems found: 634
- Hypotenuse and center
Point S is the center of the hypotenuse AB of the right triangle ABC. Calculate the area of triangle ABC if the line on the hypotenuse is 0.2 dm long and if angle ∢ACS is 30°. - 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. - Three pillars
On a straight road, three pillars are 6 m high at the same distance of 10 m. At what angle of view does Walter see each pillar if it is 30 m from the first and his eyes are 1.8 m high? - Aircraft altitude calculation
The aircraft flying just above point A can be seen from observation B, 2,400 meters away from point A, at an altitude of 52°30'. How high does the plane fly? - Diamond ABCD
In the diamond ABCD, the diagonal e = 24 cm, and the size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond. - Flowerbed
The flowerbed has the shape of an obtuse isosceles triangle. The arm has a size of 7.6 meters, and an angle opposite the base size is 124°. What is the distance from the base to the opposite vertex? - Cable car 2
The cable car rises at an angle of 16° and connects the upper and lower station with an altitude difference of 1082 m. How long is the cable car's track? - 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. - Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 13 cm, |BC| = 99 cm and angle BAD = 100° - Tower distance
How far from the lookout tower, 48 m high, did the tourist stand if he saw its top at an angle of 40°? - Tower distance angle
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? - Cable car climb
The lower station of the cable car in Smokovec is at an altitude of 1025 m, and the upper station at Hrebienk is at an altitude of 1272 m. Calculate the climb of the cable car if the horizontal distance between the slopes is 1921 m. - Tree
How tall is the tree observed at the visual angle 45°? If I stand 3 m from the tree, my eyes are two meters above the ground. - Elevation angle
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? - V-belt
Calculate the length of a belt running on two pulleys with diameters of 105 mm and 393 mm, with a centre-to-centre distance of 697 mm. - Steeple
A church tower is seen from the road at an elevation angle of 52°. When we move back a further 29 metres, it is seen at an elevation angle of 21°. How tall is the tower? - Rectangular
Rectangular triangle KLM with right angle at vertex L, angle beta at vertex K, and angle alpha at vertex M. Angle at vertex M = 65°, side l = 17.5 cm. Use Pythagorean theorems and trigonometric functions to calculate the lengths of all sides and the angle - A trapezoid
A trapezoid has a base length of a = 36.6 cm, with angles α = 60°, β = 48°, and a height of 20 cm. Calculate the lengths of the other sides of the trapezoid. - Church tower
Archdeacon church in Usti nad Labem has diverted the tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Results are written in degree minutes. - EQL triangle
Calculate the inradius and circumradius of an equilateral triangle with side a=67 cm.
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