### Quantitative Aptitude

## HEIGHT AND DISTANCE MCQs

### Total Questions : 92

**Page 1 of 5 pages**

**A flagstaff is placed on top of a building. The flagstaff and building subtend equal angles at a point on level ground which is 200 m away from the foot of the building. If the height of the flagstaff is 50 m and the height of the building is h, which of the following is true?**

__Question 1.__- h3 - 50h2 + (200)2h + (200)250 = 0
- h3 - 50h2 - (200)2h + (200)250 = 0
- h3 + 50h2 + (200)2h - (200)250 = 0
- None of these

**Answer: Option C**

**A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45Â° and 30Â° respectively. What is the height of the poster?**

__Question 3.__- $$\frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right)$$
- $$50\sqrt 3 \,{\text{m}}$$
- $$50\sqrt 3 \,{\text{m}}$$
- None of these

**Answer: Option A**

**Angles of elevation of pole are 60Â° and 45Â° from points at distances m and n on ground respectively. Here m, when measured from base of pole is less than n. What is the height of the pole?**

__Question 4.__- $$\sqrt {mn\sqrt 3 } \,{\text{units}}$$
- $$\sqrt {mn\root 4 \of 3 } \,{\text{units}}$$
- $$\sqrt {3mn} \,{\text{units}}$$
- $$\sqrt {mn} \,{\text{units}}$$

**Answer: Option A**

**A tree is cut partially and made to fall on ground. The tree however does not fall completely and is still attached to its cut part. The tree top touches the ground at a point 10m from foot of the tree making an angle of 30Â°. What is the length of the tree?**

__Question 5.__- $$10\sqrt 3 \,{\text{m}}$$
- $$\frac{{10}}{{\sqrt 3 }}\,{\text{m}}$$
- $$\frac{{\left( {\sqrt 2 - 1} \right)}}{{10}}\,{\text{m}}$$
- $$\frac{{10}}{{\sqrt 2 }}\,{\text{m}}$$

**Answer: Option A**

**Tree topâ€™s angle of elevation is 30Â° from a point on ground, 300m away the tree. When the tree grew up its angle of elevation became 60Â° from the same point. How much did the tree grow?**

__Question 6.__- $$100\sqrt 3 \,{\text{m}}$$
- $${\text{200}}\sqrt 3 \,{\text{m}}$$
- $$300\frac{1}{{\sqrt 3 }}\,{\text{m}}$$
- $$\frac{{200}}{{\sqrt 3 }}\,{\text{m}}$$

**Answer: Option B**

**Mohan looks at a tree top and the angle made is 45Â°. He moves 10 cm back and again looks at the tree top but this time angle made is 30Â°. How high is the tree top from ground?**

__Question 7.__- $$\frac{{10}}{{\sqrt 3 + 1}}\,{\text{cm}}$$
- $$20\sqrt 3 \,{\text{cm}}$$
- $$20\,{\text{cm}}$$
- $$\frac{{10}}{{\sqrt 3 - 1}}\,{\text{cm}}$$

**Answer: Option D**

**Rohit while seeing a bird on tree top made 45Â° angle of elevation. He walks 240ft. towards the tree to observe the bird closely, thus making 60Â° angle of elevation. How far was Rohit from the tree initially?**

__Question 8.__- $$\frac{{240\sqrt 3 }}{{\sqrt 3 - 1}}\,{\text{ft}}$$
- $$\frac{{240}}{{\sqrt 3 - 1}}\,{\text{ft}}$$
- $$\frac{{240}}{{\sqrt 3 }}\,{\text{ft}}$$
- $$240\sqrt 3 \,{\text{ft}}$$

**Answer: Option A**

**There is a tree between houses of A and B. If the tree leans on Aâ€™s House, the tree top rests on his window which is 12 m from ground. If the tree leans on Bâ€™s House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m, what is distance between Aâ€™s and Bâ€™s house?**

__Question 12.__- 21 m
- 25 m
- 16 m
- 12 m

**Answer: Option A**

**A and B are standing on ground 50 meters apart. The angles of elevation for these two to the top of a tree are 60Â° and 30Â°. What is height of the tree?**

__Question 14.__- $$50\sqrt 3 \,{\text{m}}$$
- $$\frac{{25}}{{\sqrt 3 }}\,{\text{m}}$$
- $$25\sqrt 3 \,{\text{m}}$$
- $$\frac{{25}}{{\sqrt 3 - 1}}\,{\text{m}}$$

**Answer: Option C**

**Raj stands in a corner of his square farm. Angle of elevation of a scarecrow placed in diagonally opposite corner is 60Â°. He starts walking backwards in a straight line and after 80ft he realizes that angle of elevation of the scarecrow now is 30Â°. What is area of the field?**

__Question 16.__- 1600 sq.ft.
- 40 sq.ft.
- $$\frac{{40}}{{\sqrt 2 }}$$ sq.ft.
- 800 sq.ft.

**Answer: Option D**

**Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30Â° and 45Â° respectively. If the lighthouse is 100 m high, the distance between the two ships is:**

__Question 18.__- 173 m
- 200 m
- 273 m
- 300 m
- None of these

**Answer: Option C**

**A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30Âº with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60Âº. What is the distance between the base of the tower and the point P?**

__Question 20.__- 4 âˆš3 units
- 8 units
- 12 units
- Data inadequate
- None of these

**Answer: Option D**

### How Do You Calculate Distance Example?

One way is to use the rate of what you are calculating and multiply it by the time it takes. This distance formula is written as d=rt d = r t . The other way to calculate distance is to use the coordinate plane. This distance equation is written as d=âˆš(x2âˆ’x1)2+(y2âˆ’y1)2 d = ( x 2 âˆ’ x 1 ) 2 + ( y 2 âˆ’ y 1 ) 2 .

### How Do You Convert Angle To Distance?

Divide the height of the object by the tangent of the angle. For this example, let's say the height of the object in question is 150 feet. 150 divided by 1.732 is 86.603. The horizontal distance from the object is 86.603 feet.

### How Do You Convert Degrees To Distance?

One degree of latitude equals approximately 364,000 feet (69 miles), one minute equals 6,068 feet (1.15 miles), and one-second equals 101 feet. One-degree of longitude equals 288,200 feet (54.6 miles), one minute equals 4,800 feet (0.91 mile), and one second equals 80 feet.

### What Are Used To Find Height Or Length Of An Object Or Distance Between Two Distant Objects?

### What Is Height And Distance Formula?

Heights and Distances,

Here, Î¸1 is called the angle of elevation and Î¸2 is called the angle of depression. For one specific type of problem in height and distances, we have a generalized formula. Height = Distance moved / [cot(original angle) â€“ cot(final angle)] => h = d / (cot Î¸1 â€“ cot Î¸2)

### What Is The Relationship Between Object Distance And Image Height?

Starting from a large value, as the object distance decreases (i.e., the object is moved closer to the lens), the image distance increases; meanwhile, the image height increases. At the 2F point, the object distance equals the image distance and the object height equals the image height.

### Does Height Affect Stride Length?

On average, adults have a step length of about 2.2 to 2.5 feet. In general, if you divide a person's step length by their height, the ratio value you get is about 0.4 (with a range from about 0.41 to 0.45).

### Does Height Relate To Distance?

The calculation of the height of an object is achieved by the measurement of its distance from the object. This includes the angle of elevation at the top of the object while calculating the height. The tangent of the angle is considered as the height of the object, which is divided by the distance from the object.

### How Do You Find Distance With Speed And Angle?

The equation for the distance traveled by a projectile being affected by gravity is sin(2Î¸)v2/g, where Î¸ is the angle, v is the initial velocity and g is acceleration due to gravity.

### How Do You Find Height From Distance?

The height of an object is calculated by measuring the distance from the object and the angle of elevation of the top of the object. The tangent of the angle is the object height divided by the distance from the object. Thus, the height is found.

### How Do You Find Height With Angle Of Elevation And Distance?

The height of an object is calculated by measuring the distance from the object and the angle of elevation of the top of the object. The tangent of the angle is the object height divided by the distance from the object. Thus, the height is found.

### How Do You Find The Distance Between Two Lines?

The formula for the distance between two lines having the equations y = mx + c1 and y = mx + c2 is: d=|c2âˆ’c1|âˆš1+m2 d = | c 2 âˆ’ c 1 | 1 + m 2 .

### How Do You Find The Height In Trigonometry?

Measure the distance from the ground to your eyeball and add the result to the result from step four to calculate the height of the object. For example, if you measure five feet from the ground to your eyeballs, you would add five to 14 to find the total height of the object equals 19 feet.

### How Do You Find Velocity With Distance And Height?

Horizontal distance traveled can be expressed as x = Vx * t , where t is the time. Vertical distance from the ground is described by the formula y = h + Vy * t â€“ g * tÂ² / 2 , where g is the gravity acceleration.

### How Do You Measure The Length Of A Pole?

It is the basic height of the shoe above the floor plus the height of the heel of the shoe.) Most experts are just too general when recommending the pole length. Few experts will mention the height of the heel of the shoe or basic height above the ground when calculating the pole length.

### What Are The Applications Of Height And Distance?

Â Height and Distance: One of the main application of trigonometry is to find the distance between two or more than two places or to find the height of the object or the angle subtended by any object at a given point without actually measuring the distance or heights or angles.

### What Is Height And Distance?

Height is the measurement of an object in the vertical direction and distance is the measurement of an object from a particular point in the horizontal direction.

### What Is The Formula For Angle Of Elevation?

Tan Î¸ = y/x; cot Î¸ = x/y. depending upon the data given in the question, corresponding formula is applied to find out the angle of elevation. Here SR is the height of man as 'l' units and height of pole to be considered will be (h - l) units.

### What Is The Height Distance?

Height is the measurement of an object in the vertical direction and distance is the measurement of an object from a particular point in the horizontal direction.

### What Is The Use Of Height And Distance In Trigonometry?

To find the height we use trigonometry because the surface of the ground, the height of Minar and the line of elevation all together form a right angle triangle with 90 degrees between the Minar and the ground. Distance is usually the 'base' of the right-angled triangle formed by the height of Minar and line of sight.

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