# Aptitude - Height & Distance Online Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to **Height & Distance**. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using **Show Answer** button. You can use **Next Quiz** button to check new set of questions in the quiz.

Q 1 - A man observes the elevation of a balloon to be 45° at a point A .He then walks towards the balloon and at a certain place B finds the elevation to be 60°. He further walks in the direction of the balloon and finds it to be directly over him at a height of 450 m. Distance travelled from A to B is

### Answer : A

### Explanation

450/BD= tan (60) =>BD =450/√3 450/AD= tan (30) =>AD= 450√3 AD =BD +AB =>AB=AD-BD= 450√3-450/√3=(450x3-450)/√3=300√3m

Q 2 - When the sun's altitude changes from 45° to 60°, the length of the shadow of a tower decreases by 45m. What is the height of the tower?

### Answer : A

### Explanation

Let AD be the tower, BD be the initial shadow and CD be the final shadow. Given that BC = 45 m, ABD = 45°, ACD = 60°, Let CD = x, AD = h From the right CDA, tan60=h/x From the right BDA, tan45=(45+x)/h=>h=45+x =>h=45+h/√3 =>h(1-1/√3)=45 =>h=45/(1-1/√3)=(45√3)/(√3-1)

Q 3 - A man in a boat is rowing away from a cliff (180 meters high), take 90 seconds to change angle of elevation of the top of cliff from 30° to 45°.The speed of the boat is

### Answer : C

### Explanation

From right angled triangle ADB, Tan45=AB/AD =>AB=AD=180 From right angled triangle ACB, Tan 30=180/(CD+180) =>CD+180=180√3 =>CD=180(√3-1) Speed =Distance/Time=180(√3-1)/90=2(√3-1) m/sec

Q 4 - A step inclining toward a vertical divider makes a point of 45 with the even ground. The step's Foot is 3m from the divider. Find Length of the step?

### Answer : A

### Explanation

Let AB be the step and BC be the divider and let AC be the even ground. Then, ∠CAB=45 and AC=3m. Let AB= x Meter. From right △ ACB, we have AB/AC =sec. 45° = √2 => x/3 = √2 X= 3√2m = (3*1.41) m= 4.23m. ∴ Length of the stepping stool is 4.23 m

Q 5 - From The highest point of a 10 m high building, the edge of rise of the of the highest point of a tower is 60° and the despondency's edge of its foot is 45°,Find The tower's stature. (take√3=1.732)

### Answer : D

### Explanation

Let AB be the building and CD be the tower. Draw BE perpendicular to CD. At that point CE =AB = 10m, ∠EBD= 60° and ∠ACB= ∠ CBE=45° AC/AB= cot45°=1 = >AC/10 =1 => AC = 10m. From △ EBD, we have DE/BE= tan 60°=√3 => DE/AC= √3 => DE/10= 1.732 =>DE = 17.3 Height of the tower = CD= CE+DE= (10+17.32) = 27.3 m.

Q 6 - A 10 m long stepping stool is put against a divider. It is slanted at a point of 30°to the ground. The separation of the stepping stool's foot from the divider is:

### Answer : C

### Explanation

Let AB be the step slanted at 30°to the Ground AC. Then, AB=10m and

Q 7 - A kite is flying at a tallness of 75 m from the level of ground, joined to a string slanted at 60° to the level. The string's length is:

### Answer : B

### Explanation

Let AB be the kite and AC be the level ground So that BC - AC. At that point, ∠BAC=60°and BC=75m. Let AB=x meters. Presently AB/BC=coses60°=2/ √3 => x/75=2/√3 =>x=150/√3 =150* √3/3=50 √3m. ∴ Length of the string=50 √3m.

Q 8 - The stature of a tree is 10m. It is twisted by the wind in a manner that its top touches the ground and makes a point of 60 with the ground. At what range from base did the tree get twisted? (√3=1.73)

### Answer : A

### Explanation

Let AB be the tree bowed at the point C so that part CB takes the position CD. Then ,CD=CB. Let AC=x meters. At that point, CD = CB= (10-X) m and ∠ADC=60°. AC/AC=sin60° => x/(10-x) = √3/2 =>2x=10 √3-√3x => (2+ √3) x= 10 √3 =>x=10 √3/ (2+ √3)*(2-√3)/(2-√3)=20 √3-30)m = (20*1.73-30) m=4.6m => Required height=4.6m.