If the ratio of the height of a tower and the length of its shadow is `sqrt3:1`, what is the angle of elevation of the Sun? Show
Let C be the angle of elevation of sun is θ.  Given that: Height of tower is `sqrt3` meters and length of shadow is 1. Here we have to find angle of elevation of sun. In a triangle ABC, `⇒ tanθ =(AB)/(BC)` `⇒ tan θ=sqrt3/1` ` [∵ tan 60°=sqrt3]` `⇒ tan θ=sqrt3` `⇒ θ=60 °` Hence the angle of elevation of sun is 60°. Concept: Heights and Distances Is there an error in this question or solution?
Solution: In the figure AB is the tower BD and BC are the shadow of the tower in two situations Consider BD = x m and AB = h m In triangle ABD tan 450 = h/x So we get 1 = h/x h = x ….. (1) In triangle ABC tan 300 = h/(x + 10) So we get 1/√3 = h/(x + 10) Using equation (1) h√3 = h + 10 h (√3 – 1) = 10 We know that h = 10/(√3 – 1) It can be written as h = [10 (√3 + 1)]/ [(√3 – 1) (√3 + 1)] By further calculation h = (10√3 + 1)/ 2 So we get h = 5 (1.73 + 1) h = 5 × 2.73 h = 13.65 m Therefore, the height of the tower is 13.65 m.
Guys, does anyone know the answer? get from the top of a multi-storeyed building, 90m high, the angles of depression of the top and the bottom of a tower are observed to be 300 and 600 respectively. find the height of the tower? from screen. From the top of a tower, the angle of depression of the top and bottom of a multistoreyed building are 30 ^o and 60 ^o respectively. If the height of the building is 100m. Find the height of a tower.Click here👆to get an answer to your question ✍️ From the top of a tower, the angle of depression of the top and bottom of a multistoreyed building are 30 ^o and 60 ^o respectively. If the height of the building is 100m. Find the height of a tower. Question o and 60 o respectively. If the height of the building is 100m. Find the height of a tower. Let AC=h be the height of the tower.Medium Open in App Solution Verified by Toppr and ED be the multi-storeyed building, where ED=100m So, ED=BC=100m So, AB=(h−100)m In ΔABE, tan30 o = EB AB ⇒ 3 1 = EB h−100 ⇒EB= 3 (h−100) .... (i) So, DC=EB= 3 (h−100) In ΔADC, tan60 o = DC AC = 3 = 3 (h−100) h ⇒3(h−100)=h ⇒3h−300=h ⇒2h=300 ⇒h=150 metres Thus, the height of the tower is 150 m. Video Explanation Solve any question of Some Applications of Trigonometry with:- Patterns of problems > Was this answer helpful? 3 0 अधिक देखने के लिए क्लिक करें स्रोत : www.toppr.com From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is from Quantitative Aptitude Heights and DistancesFrom figure,In Δ CDE, ...(i)In Δ ABE, Put the value of in eq. (i) Heights and DistancesMultiple Choice Questions41. Two persons are on either side of a temple, 75 m high, observe the angle of elevation of the top of the temple to be 30° and 60° respectively. The distance between the persons is 173.2 m 100 m 157.7 m 273.2 m 61 Views Answer 42. A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time, a tower casts a shadow 40 m long on the ground. The height of the tower is 60 m 65 m 70 m 72 m 51 Views Answer 43. If the elevation of the Sun changes from 30° to 60°, then the difference between the lengths of shadows of a pole 15 m high, is 7.5 m 15 m 41 Views Answer 44. The tops of two poles of height 24 m and 36 m are connected by wire. If the wire makes an angle of 60° with the horizontal, then the length of the wire is 8 m 6 m 48 Views Answer 45. A 1.6 m tall observer is 45 m away from a tower. The angle of elevation from his eye to the top of the tower is 30°, then the height of the tower (in m) is: 25.98 26.58 27.58 m 27.98 74 Views Answer 46. When the angle of elevation of the sun increases from 30° to 60°, the shadow of a post is diminished by 5 m. Then, the height of the post is 41 Views Answer 47. A man standing in one corner of a square football field observes that the angle subtend by a pole in the corner just diagonally opposite to this corner is 60°. When he retires 80 m from the corner, along the same straight line, he finds the angle to be 30°. The length of the field is 20 m 40 m 45 Views Answer Zigya App 48. From the top of a cliff 90 m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 60° respectively. The height of the tower is 60 m 75 m 30 m 45 m A. 60 m From figure, In Δ CDE, ...(i) In Δ ABE, Put the value of in eq. (i) 61 Views Switch Flag Bookmark 49. From the top of a building 60 m high, the angle of depression of the top and bottom of a tower are observed to be 30° and 60°. The height of the tower (in metre) is: 40 45 50 55 56 Views Answer 4 5 अधिक देखने के लिए क्लिक करें स्रोत : www.zigya.com [Solved] From the top of a cliff 90 m high, the angle of depression oGiven: As shown in the above figure, AB = 90 m, AB is the given cliff DC is the tower on which the angle of depression is given. The angle of depression of Home Quantitative Aptitude Trigonometry Heights and Distances QuestionDownload Solution PDF From the top of a cliff 90 m high, the angle of depression of the top and bottom of a tower are 30∘ and 60∘ respectively, then the height of the tower is -This question was previously asked in RSMSSB LDC Official Paper 1 (Held on : 16 Sept 2018) Download PDF Attempt Online View all RSMSSB LDC Papers > 30 m 30√3 m (90 - 30√3) m 60 m Answer (Detailed Solution Below)Option 4 : 60 m Free TestsView all Free tests > FREE RSMSSB LDC Official Paper 1 (Held on : 12 Aug 2018) 2875 150 Questions 100 Marks 180 Mins Start Now Detailed SolutionDownload Solution PDF Given:As shown in the above figure, AB = 90 m, AB is the given cliff DC is the tower on which the angle of depression is given. The angle of depression of the top and bottom of the tower is 30° and 60°. Calculation:Consider the triangle Δ ABC, ⇒ Tan60° = √3/1 = AB/ BC ⇒ BC = 90/√3 = 30×√3 m ----(1) Consider the triangle Δ ADE, ⇒ Tan30° = 1/√3 = AE/DE (As DE = BC) ⇒ AE = 30 m ----(2) Now, DC = AB – AE ⇒ DC = 90 – 30 = 60 m ∴ DC is 60 mDownload Solution PDF Share on Whatsapp India’s #1 Learning Platform Start Complete Exam Preparation Daily Live MasterClasses Practice Question Bank Mock Tests & Quizzes Get Started for Free Download App Trusted by 2,71,00,511+ Students ‹‹ Previous Ques Next Ques ›› More Heights and Distances QuestionsQ1. The difference in the lengths of the shadows of a 10 m high pole when the angles of elevation of the sun are 30° and 60° is:Q2. A 20 m tall tower makes an angle of depression of 30° with the top of a pole and an angle of depression of 60° with the foot of the pole. How tall is the pole?Q3. The difference in the lengths of the shadows of a pole cast by the sun (at different times of a day) when the angles of elevation of the top of the pole measured from two points on the ground on the same side of the pole were 45° and 30° was given as10(3−1)m. How tall was the pole? Q4. The distance of the foot of a 20 m high tower from a point on the ground is 20√3 m. What is the angle of elevation of the top of the tower from this point?Q5. The difference in the lengths of the shadows of a pole cast by the sun (at two different times of the day) when the angles of elevation of the top of the pole measured from two points on the ground on the same side if the pole were 60° and 30° was given as2033 m, How tall was the pole? Q6. A ladder 10 m long rests against a vertical wall making an angle of 30° with the wall. How high up (in m) does it reach the wall from the ground? (Take3=1.73.) Q7. The angle of elevation of a ladder against a wall is 45°. The length of the ladder is 12 m. What is the distance between the wall and the foot of the ladder?Q8. Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, then the distance between their top is:-Q9. The angles of elevation of the top of the tower from two points on the ground at a distance of 18 m and 32 m from the foot of a tower are complementary. The height of the tower isQ10. The distance between two poles of length 16 metres and 4 metres respectively, is y meters. If two angle of elevation of their respective top from the mid-point are complementary to each other than the value of y is -More Trigonometry QuestionsQ1. If sin A + sin2 A = 1 then what is the value of cos2 A + cos4 A?Q2. The difference in the lengths of the shadows of a 10 m high pole when the angles of elevation of the sun are 30° and 60° is:Q3. A 20 m tall tower makes an angle of depression of 30° with the top of a pole and an angle of depression of 60° with the foot of the pole. How tall is the pole?Q4. The difference in the lengths of the shadows of a pole cast by the sun (at different times of a day) when the angles of elevation of the top of the pole measured from two points on the ground on the same side of the pole were 45° and 30° was given as10(3−1)m. How tall was the pole? Q5. The distance of the foot of a 20 m high tower from a point on the ground is 20√3 m. What is the angle of elevation of the top of the tower from this point?Q6. The difference in the lengths of the shadows of a pole cast by the sun (at two different times of the day) when the angles of elevation of the top of the pole measured from two points on the ground on the same side if the pole were 60° and 30° was given as2033 m, How tall was the pole? Q7. The value of1 − sinθ1 + sinθ is - Q8. In a triangle ABC, right-angled at C, ifsecA=135 , then find the value of 1+sinAcosB. Q9. Evaluate the following expression.tan260∘+cosec30∘sin90∘+3sec230∘4sin245∘+sec260∘−cot230∘−5cos290∘ Q10. If cosec2 θ (cos θ - 1)(1 + cos θ) = k, then what is the value of k?अधिक देखने के लिए क्लिक करें स्रोत : testbook.com |
When the angle of elevation of the sun increases from 300 to 600 the shadow of a post is diminished by 5 Metres then height of the post is in Metres?
zusammenhängende Posts
Urheberrechte © © 2024 frojeostern Inc.
