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Intelligence Quotient(IQ)

Height and Distance (Numerical Reasoning Test)

By Admin
12/4/2024
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Fundamental concepts before going through the topic (विषय मार्फत जानु अघि आधारभूत अवधारणाहरू)

Concept 1(अवधारणा १)

revise.png
  • Similar(~) triangles will also follow the same ratio; For Example: In the Figure below figure 1 is in the ratio 3:4:5 and we can compare figure 2 with figure 1 as 6 is the multiple of 3 and 10 is the multiple of 5 and both are multiple of 2. Therefore figure (ii) should also follow the same rule as (समान (~) त्रिभुजहरूले पनि समान अनुपात पछ्याउनेछन्; उदाहरणका लागि: तलको चित्रमा चित्र १ को अनुपात ३:४:५ मा छ र हामीले चित्र १ सँग चित्र २ तुलना गर्न सक्छौँ किनकि ६ को ३ को गुणन हो र १० भनेको ५ को गुणन हो र दुबै २ को गुणन हो। त्यसैले चित्र (ii) ले पनि सोही नियमको पालना गर्नुपर्छ)
    3*2:4* 2:5*2 = 6:8:10
  • Directly the value of remaining portion will be 8 and same continues in other figures. (सीधै बाँकी भागको मूल्य 8 हुनेछ र अन्य अंकहरूमा उही जारी छ)

Screenshot 2024-12-02 192859.png

Concept 2 (अवधारणा २):

  • In any right angled triangle longest leg should be hypotenuse.(कुनै पनि समकोण त्रिकोणमा सबैभन्दा लामो खुट्टा कर्ण हुनुपर्छ।)
  • Opposite of greater angle in any triangle should have the greater side and smaller will have small side. (कुनै पनि त्रिभुजमा ठूलो कोणको विपरित पक्ष ठूलो र सानोको सानो पक्ष हुनुपर्छ।)
  • Oftenly the problems will be asked when the angle of elevation or depression will be 30°, 45° and 60°. (प्रायः समस्याहरू सोधिनेछन् जब उचाइ वा अवसादको कोण 30°, 45° र 60° हुनेछ।)
  • In any right angled triangle if one side is 45° then remaining will automatically be 45°(कुनै पनि समकोण त्रिभुजमा यदि एउटा भुजा ४५° छ भने बाँकी स्वतः ४५° हुनेछ)

(i.e. 90°+45°+x=180°; x=45°)

  • In any right angled triangle if one side is 60° then remaining will automatically be 30°. (कुनै पनि समकोण त्रिभुजमा यदि एउटा भुजा ६०° छ भने बाँकी स्वतः ३०° हुनेछ।)

Prerequisite

  • How to find Square Root? (स्क्वायर रूट कसरी पत्ता लगाउने?)
  • Sum of interior angle of triangle is 180°. (त्रिभुजको भित्री कोणको योगफल 180° हो)
  • Table given below is very lengthy process and need to remember alot of information. (तल दिइएको तालिका धेरै लामो प्रक्रिया हो र धेरै कुरा सम्झनु आवश्यक छ।)
  • Remembering table given below is strictly prohibited.

30°

45°

60°

90°

Remarks

0

1

2

3

4

(write from 0 to 4)

√(0/4)

√(1/4)

√(2/4)

√(3/4)

√(4/4)

divide by 4 and make root of each

Sin

0

1/2

1/√2

√3/2

1

simplify

Cos

1

√3/2

1/√2

1/2

0

rotate the simplified value of sin from 90 to 0

Tan

0

1/√3

1

√3

divide sin/cos

Cosec

2

√2

2/√3

1

1/ sin

Sec

1

2/√3

√2

2

1/cos; or rotate cosec 90 to 0 for sec 0 to 90 respectively

Cot

√3

1

1/√3

1

1/ tan

  • This will also follow certain rule as shown in the figure below: (तलको चित्रमा देखाइए अनुसार यसले निश्चित नियमहरू पनि पालन गर्नेछ:)
  • You can solve all the problems just by remembering figure below:
Screenshot 2024-12-02 194635.png

Example

  1. 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 30° and 45° respectively. If the lighthouse is 100 m high, the distance between the two ships is: (एउटा लाइटहाउसको दुई छेउमा समुद्रमा दुईवटा जहाज चलिरहेका छन्। लाइटहाउसको शीर्षको उचाइको कोण जहाजबाट अवलोकन गरिन्छ क्रमशः 30° र 45° हो। यदि लाइटहाउस 100 मिटर अग्लो छ भने, दुई जहाजहरू बीचको दूरी हो:)

a. 173 m

b. 200 m

c. 273 m

d. 300 m

Screenshot 2024-12-02 195954.png

In the figure above (माथिको चित्रमा)

  • From triangle ABD given angle is 45°; therefore the height and base will be equal. (त्रिभुज ABD बाट दिइएको कोण 45° छ; त्यसैले उचाइ र आधार बराबर हुनेछ।)
  • From another triangle ACB angle is 30°; therefore the height will be a= 100 and base =a√3= 100√ 3. Therefore both the ships are (अर्को त्रिकोणबाट ACB कोण 30° हो; त्यसैले उचाइ a=100 र आधार =a√3= 100√ 3 हुनेछ। त्यसैले दुबै जहाजहरू)

100√3 m+100m apart(टाढा)

i.e. more than 200 and less than 300 should be correct option. (अर्थात् 200 भन्दा बढी र 300 भन्दा कम सही विकल्प हुनुपर्छ)

  • C is the correct option.(C सही विकल्प हो।)

2. The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is:

a. 2.3 m

b. 4.6 m

c. 7.8 m

d. 9.2 m

2.png

3. An observer 1.6 m tall is 20 √3 away from a tower. The angle of elevation from his eye to the top of the tower is 30°. The height of the tower is:

a. 21.6 m

b. 23.2 m

c. 24.72 m

d. None

3.png

4. From a point P on a level ground, the angle of elevation of the top tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is:

a. 149 m

b. 156 m

c. 173 m

d. 200 m

Q4.png

5. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:

a. 30°

b. 45°

c. 60°

d. 90°

5.png

Note: Questions will simply be logical and easy to do without calculator.

नोट: प्रश्नहरू केवल तार्किक र क्याल्कुलेटर बिना गर्न सजिलो हुनेछ।

For more clearer view of this topic you can go through this video.(यस विषयको थप स्पष्ट दृश्यको लागि तपाइँ यो भिडियो मार्फत जान सक्नुहुन्छ।)