A straight line drawn on the horizontal plane is called a—
- avertical line
- bhorizontal line
- cinclined line
- dperpendicular line
160 questions · 27 sections
A straight line drawn on the horizontal plane is called a—
A straight line parallel to the horizon is also called a—
A line perpendicular to the horizontal plane is called a—
A vertical line is also known as a—
When a horizontal line and a vertical line intersect at right angles on a plane, the plane they define is called the—
The vertical plane is perpendicular to the—
In the standard tree figure with vertical and on the ground, the segment represents the—
In the same figure, represents the—
The plane formed by points , , where is the vertical tree and is on the ground is a—
Two horizontal lines drawn in the same plane are always—
"Normal line" with respect to the horizontal plane means a line that is—
A flagpole standing erect on level ground best represents a—
The angle formed at the observer's eye by the line of sight to a point above the horizontal line is called the—
The angle of elevation is always measured from the—
In the textbook figure where lies on the horizontal line and lies above , the angle of elevation of at is—
Looking up at the top of a tower from a point on the ground produces an angle of—
The theoretical maximum value of an angle of elevation is—
If the angle of elevation of an object is , the object lies on the—
As an observer moves towards the foot of a tower (on level ground), the angle of elevation to its top—
The angle of elevation of an object is when the object is—
If the sun is directly overhead, the angle of elevation of the sun is—
The angle of elevation of the top of a hill is greater for an observer who is—
The angle formed at the observer's eye by the line of sight to a point below the horizontal line is called the—
From the top of a tower, the angle to a point on the ground is an angle of—
An aeroplane flying high looks down at a building on the ground; the angle from the plane is one of—
The angle of depression from a higher point and the angle of elevation back to that point are equal because they form—
If the angle of depression of a point from the top of a tower is , the angle of elevation of the tower top from that point is—
As an observed point on the ground moves further from the foot of a tall building, the angle of depression from the top—
The angle of depression equals when the line of sight is—
The angle of depression to the foot of a vertical pole, observed from directly above its top, is—
While drawing a angle for a problem, the figure should approximately satisfy—
While drawing a angle, the figure should approximately satisfy—
While drawing a angle, the figure should approximately satisfy—
In a right triangle with one acute angle , the side opposite to that angle is—
In a right triangle with one acute angle , the side opposite to that angle is—
In a –– triangle, the two legs are—
With the height of a tower, m the horizontal distance, and , the equation equals—
Therefore the height satisfies—
Numerically equals—
After rationalizing, becomes—
The approximate height of the tower in Example 1 is—
To rationalize , the numerator and denominator are multiplied by—
In Example 2, with tree m, foot distance , and , equals—
The distance satisfies—
simplifies to—
The approximate ground distance of the point in Example 2 is—
The relation tells us that the side opposite the angle is times the—
With the same height m, if the elevation were instead of , the foot distance would be—
A ladder of length m leans against a wall making with the ground; with m and wall height , equals—
Therefore the wall height equals—
in surd form equals—
The approximate wall height in Example 3 is—
The horizontal distance from the foot of the wall to the foot of the ladder is—
In a –– right triangle, the two legs are—
The stick contacts the tree at m above the ground; the depression angle at the contact is . By alternate angles, equals—
From right with stick as hypotenuse, equals—
Therefore equals—
The length of the stick in Example 4 is—
The reasoning that the depression angle at equals at uses the fact that the two horizontal lines at and at are—
Angle of depression from a higher point and angle of elevation from a lower point form—
Building height , , with . Then equals—
From the equation , we get
Moving back m to point gives elevation , so equals—
Therefore also equals—
Combining gives
Hence approximately equals—
Rationalizing, is equivalent to—
As the observer moves backwards on level ground, the angle of elevation of a fixed building top—
The pole stands , breaks without separation, and the broken piece slopes down to at distance m, with . From , equals—
Solving for the standing piece, equals—
Numerically equals—
From the same triangle, equals—
So the broken piece equals—
The total height of the pole is approximately—
The unbroken (still standing) piece measures approximately—
The slanted (broken) piece measures exactly—
A balloon flies above a point between two posts km apart on level ground. From the balloon, the depression of the nearer post is and the farther post . With balloon height , the distance to the foot of the post is—
The horizontal distance to the foot of the post equals—
The two horizontal distances together equal the spacing between the posts—
Solving gives
Approximate height of the balloon above the ground in metres—
From the top of a house, the angle of depression to a point on the ground m from the foot is . The angle of elevation from that point to the top equals—
The equation gives
is approximately—
After rationalization, becomes—
Initial elevation of tower top is at with . Then equals—
After moving m back to point where elevation is , equals—
Combining the two equations gives
Then equals—
The approximate height of the tower is—
From the initial point , elevation of the minar top is . The distance to the foot equals—
After moving m towards the minar, the new distance to the foot equals—
Combined equations give—
The approximate height of the minar is—
The exact (rationalized) form equals—
With initial distance to the tower and elevation , equals—
After moving m back, equals—
Solving the two equations gives
The tower height m is approximately—
The width of the river (from observer to opposite bank under tower) equals—
With standing piece and broken (slanting) piece falling from the break to the ground, the original pole length satisfies—
The vertical drop of the break equals the standing piece, giving
Substituting and solving gives
The approximate length of the broken piece is—
The rationalized form equals—
With standing piece and slanting piece touching ground at where m and , gives
Numerically is approximately—
From , the slanting piece equals—
The total height of the original tree is—
Approximately, the tree was—
The other name of the horizontal line (geo-line) is—
In a figure where and lie on a horizontal line above, and on a horizontal line below, and is the transversal, consider:
The relation in the above figure holds because the two horizontal lines are—
The pair of angles between line of sight and horizontal at the two endpoints of the line of sight are—
A m ladder leans against a wall making with the ground. The height it reaches on the wall equals—
equals—
The wall is m tall, so the ladder top is below the wall top by—
approximately equals—
A tree breaks; the broken part forms with the ground touching at m from the base. The standing piece equals—
From , the broken piece equals—
The total height of the tree is approximately—
The angle of elevation from a point on the ground to a point above the ground is the angle—
If the height of a pole is times the length of its shadow, then equals—
Therefore the angle of elevation of the sun is—
A m ladder makes with the ground, touching the top of a wall. The wall height equals—
m approximately equals—
equals—
equals—
equals—
The shadow of a vertical pole on level ground is longest when the sun's elevation is—
From a building, the angle of depression of a car on level ground is . The horizontal distance of the car from the foot equals—
From the same observation point on the ground, the angle of elevation of a fixed tower top is determined uniquely by the geometry, so changing the angle while keeping the point and tower fixed is—
In a right triangle with one acute angle , is maximum at
Trigonometric ratios are independent of the size of a right triangle because of the—