Goniometry and trigonometry - practice problems - page 9 of 28
Number of problems found: 558
- Two groves
Two groves A B are separated by a forest. Both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B if AC = 5004 m, BC = 2600 m, and angle ABC = 53° 45'? - A construction
A construction worker is trying to find the height of a skyrise building. He is standing some distance away from the base with an angle of elevation of 65 degrees. The worker moves 50 feet closer and measures the angle of elevation to be 75 degrees. Find - Determine 81756
The area for shooting training has the shape of a trapezoid, the parallel sides of which are 36m, 21m long, and the remaining sides are 14m, 16m long. Determine the size of the interior angles with a longer base. - Horizontally 6296
The camera with a viewing angle of 120 ° was placed horizontally on the observatory at 30 m. What length d of the section at the tower's base can the camera not capture? - Determine 83081
A paper kite is shaped like a deltoid ABCD, with two shorter sides 30 cm long, two longer sides 51 cm long, and a shorter diagonal 48 cm long. Determine the sizes of the internal angles of the given deltoid. - Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm, u2 = 12 cm, and the angle formed by them is 30 degrees. - Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - Loonie
Loonie has three wooden sticks measuring 17 inches, 21 inches, and 25 inches. He lays them down to form a triangle. Find the measure of the angle enclosed by 17 inches and 21 inches. (Express answers to the nearest hundredths) (using the law of cosines) - Centre of the hypotenuse
The interior angles of the triangle ABC, alpha, beta, and gamma are in a ratio of 1:2:3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB. - Parallelogram
The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Parallelogram 65334
In a parallelogram, the sum of the lengths of the sides a+b = 234. The angle subtended by the sides a and b is 60°. The diagonal size against the given angle of 60° is u=162. Calculate the sides of the parallelogram, its perimeter, and its area. - Parallelogram ABCD
We have the parallelogram ABCD, where AB is 6.2 cm BC is 5.4 cm AC is 4.8 cm calculate the height on the AB side and the angle DAB - Triangle's centroid
In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid), and the point S is the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side t - A flagpole
A flagpole is leaning at an angle of 107° with the ground. A string fastened to the top of the flagpole is holding up the pole. The string makes an angle of 38° with the ground, and the flagpole is 8 m long. What is the length of the string? - Power line pole
From point A, the power pole is visible at an angle of 18 degrees. From place B, which we reach if we go from place A 30m towards the pillar at an angle of 10 degrees. Find the height of the power pole. - Approaches 45521
The observer lies on the ground at a distance of 20m from a hunting lodge 5m high. A) At what angle of view does the posed see? B) How much does the angle of view change if it approaches the sitting by 5m? - Magnitude 25411
There is a circle with a radius of 10 cm and its chord, which is 12 cm long. Calculate the magnitude of the central angle that belongs to this chord. - Observation 63194
Determine the height of the cloud above the lake's surface if we see it from place A at an elevation angle of 20° 57'. From the same place A, we see its image in the lake at a depth angle of 24° 12'. Observation point A is 115m above the lake level. - Diagonal BD
Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42° - Observation tower
The observation tower has a height of 105 m above sea level. The ship is aimed at a depth angle of 1° 49' from the tower. How far is the ship from the base of the tower?
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