Tangent - practice problems
Tangent is a trigonometric function. In a rectangular triangle, it is the ratio of the opposite and adjacent side to a given internal angle. Algebraically is defined as the ratio of the sine and cosine of a given angle. It is periodic with a period of π = 180 °.Number of problems found: 314
- 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? - Building shadow
When the Sun's altitude is 30° above the horizontal, find the length of the shadow cast by a 50 m high building. - 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. - Angle over circle
In the figure, O is the centre of the circle and AB is tangent to the circle at B. If angle OAB is 28°, find angle AOB. The figure is not to scale. - Angle of inclination
Find the angle of inclination of a ramp that rises 80 cm over a horizontal length of 200 cm. - 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. - A tree 3
A tree breaks due to a storm and the broken part bends so that the top of the tree touches the ground at an angle of 30°. The distance from the foot of the tree to the point where the top touches the ground is 8 m. Find the original height of the tree. - 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 - Angle and slope
Find the angle between the x-axis and the line joining the points (3, −1) and (4, −2). - 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 - 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. - 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. - 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 - 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 lighthouse
A lighthouse overlooks a bay, and it is 77 meters high. From the top, the lighthouse keeper can see a yacht southward at an angle of depression of 32 degrees and another boat eastward at an angle of 25 degrees. What is the distance between the boats? - The apothem
The apothem of a regular hexagon is 5√3 inches. Find one of its sides and area. - One side 4
One side of a regular octagon is 12 inches. Find the apothem and its area. - A boy 5
A boy starts at A and walks 3 km east to B. He then walks 4 km north to C. Find the bearing of C from A. - 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 - 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.
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