Goniometry and trigonometry - practice problems
Goniometry and trigonometry study relationships between angles and sides in triangles and circular functions. Core concepts include the six trigonometric ratios (sine, cosine, tangent, cosecant, secant, cotangent), the unit circle definition extending trig functions to all angles, and trigonometric identities like Pythagorean, sum/difference, and double-angle formulas. Applications include solving right and oblique triangles using the Law of Sines and Law of Cosines.Number of problems found: 633
- Angle of elevation
The angle of elevation of the top of an unfinished pillar at a point 150 m from its base is 30°. If the angle of elevation at the same point is to be 45°, then the pillar has to be raised to a height of how many meters? - A radio antenna
Avanti is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof (point A) is 42°, and the angle of elevation from - Angle of inclination
Find the angle of inclination of a ramp that rises 80 cm over a horizontal length of 200 cm. - An electrician 7
An electrician has to repair an electric fault on a pole 4 meters in height. He needs to reach a point 1 m below the top. What should be the length of the ladder that he could use, when inclined at an angle 60° to the horizontal? - Elevation angle
A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60°, and angle of depression of the base of the hill is 30°. Find the distance of the hill from the ship and the height of t - A kite 3
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in th - RT with rectangle
In the diagram, find the lengths h and b. One rectangle and one right triangle share one side. We know two angles and the length of the common side, as shown in the picture. - Triangle 97
Triangle DEF with angle Ê = 40°, angle F = 90°, EF = 45 mm. Find the length of DE. - The tent 3
The top of a 1.3 meters tall tent is tethered to the ground by a cable. The cable makes a 37 degrees angle with the ground. Find the cable length. - One side 4
One side of a regular octagon is 12 inches. Find the apothem and its area. - A right
A right triangle has side lengths a=3, b=5, and c=4, as shown below. Use these lengths to find tan x, sin x, and cos x. - Three angles
Find all missing angle values using the Law of Cosines, given all three sides: a = 12, b = 13, and c = 20 - X-triangle
Find the length of the x segment in the given triangle drawings. - Tower + pole
On horizontal ground, there is a vertical tower with a flagpole on its top. From a point 9 m from the foot of the tower, the angles of elevation of the top and bottom of the flagpole are 60° and 30° respectively. Find the height of the flagpole. - Two men 2
Two men are on opposite sides of a tower. They measure the angles of elevation of the top of the tower as 30° and 45°, respectively. If the height of the tower is 50 m, find the distance between the two men. - The shadow 2
The shadow of a tower standing on level ground is found to be 40 m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower. - Triangle 90
A triangle has sides of 6 cm, 4.5 cm, and 7.5 cm. What are the sizes of its angles? - Angle of elevation
From a point A on the ground, the angle of elevation of the top of a 20 m tall building is 45°. A flag is hoisted at the top of the building, and the angle of elevation of the top of the flagpole from A is 60°. Find the length of the flagpole and the dist - Angle of elevation 3
The angle of elevation of a pole from a point on the horizontal ground is 15°. After moving 10 m closer to the pole, the angle of elevation becomes 30°. What is the height of the pole? - The angle 9
The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving 20 m closer to the foot of the tower to a point B, the angle of elevation increases to 60°. Find the height of the tower and the distance of the tower from point A
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