[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-342420-105":59,"doc-detail-342420-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","angle-of-elevation-and-angle-of-depression-examples-and-practice","Angle of Elevation and Angle of Depression - Examples and Practice","","A set of worked geometry problems focuses on angle of elevation and angle of depression using trigonometric relationships. The examples compute tree height, sun elevation angle, distances from an elevated observer to ships, and the range from a lighthouse top to a boat, including airplane takeoff and in-air travel. A practice/homework section extends these ideas with additional scenarios, rounding requirements, and mixed units such as feet, meters, and yards.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/angle-of-elevation-and-angle-of-depression-examples-and-practice/342420/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/angle-of-elevation-and-angle-of-depression-examples-and-practice/342420.png","ImageObject",300,407,{"name":92,"@type":93},"Olivia Brown","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-24","2026-09-22",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find a tree’s height from an angle of elevation and a horizontal distance?","Question",{"text":112,"@type":113},"Use the given horizontal distance and the angle of elevation to form a right triangle, then apply a trigonometric function (typically tangent) to solve for height, rounding as instructed.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is an angle of depression and how is it used to find distances to an object below?",{"text":117,"@type":113},"Angle of depression is measured from a higher viewpoint down to a lower object. You pair the angle with the horizontal distance or use relationships from a right triangle to compute the required distance, rounding to the specified unit.",{"name":119,"@type":110,"acceptedAnswer":120},"Why do these problems specify different rounding targets such as the nearest degree or nearest foot?",{"text":121,"@type":113},"Each problem requires a particular precision for the final answer. The rounding rule ensures the distance or angle is reported in the correct level of accuracy requested by the question.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},342420,1790269094,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":14,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":46},16904993612988,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","# Angle of Elevation and Angle of Depression\n\nExample 1  \n   \nAt a point on the ground 40 feet from the foot of a tree,the angle of elevation of the top ofthe tree is 42°.Find the height of the tree,to the nearest tenth of a foot  \nExample 2  \n   \nFind,to the nearest degree,the angle of elevation of the sun when a vertical post 15 feet highcasts a shadow which is 20 feet long.  \nExample 3  \nAn observer in a balloon,which is 2000 feet above an airport,finds that the angle of  \ndepression of a steamer ship out at sea is 21 degrees.Find,to the nearest hundred feet,thedistance between the observer in the balloon and the steamer ship at sea.  \nExample 4  \nFrom the top of a lighthouse 160 feet high,the angle of depression of a boat out at sea is 24°.Find,to the nearest foot,the distance from the boat to the foot of the lighthouse.(The footof the lighthouse is at sea level.)  \nExample 5  \nAn airplane which had taken off from an airport traveled aground distance(horizontal)of  \n3,660 feet.What is the angle of elevation from the point of take-off to the point when theplane has traveled 4,150 feet through the air?Round to the nearest degree.  \n## Practice /Homework\n\n1.  A tree casts a60 foot shadow.The angle of elevation is 30°.This is the angle at whichyou look up to the top of the tree from the ground.What is the height of the tree?  \n2.   An observer is 120 feet from the base of a television tower which is 150 feet tall.Find,to the nearest degree,the angle of elevation of the top of the tower from the pointwhere the observer is standing.  \n3.  From the top of a vertical cliff which is 40 meters high,the angle of depression of anobject that is level with the base of the cliff is 34°.How far is the object from thebase of the cliff,to the nearest meter?  \n4.  From the top of a cliff which is 450 feet above sea level,the angle of depression of aboat out at sea is 24 degrees.Find,to the nearest foot,the distance from the top ofthe cliff to the boat.  \n5.  The angle of elevation of the top of a flagpole from a point on the ground 30 metersfrom the base of the flagpole is 18 degrees.What is the height of the flagpole,to thenearest meter?  \n6.  An airplane is flying at an altitude of 1000 meters.From the plane,the angle ofdepression to the base of a tree on the ground is measured as 15°.What is the distancefrom the plane to the base of the tree,rounded to the nearest tenth of a meter?  \n7.  \nFrom a 200 feet high cliff a boat isnoticed floundering at sea!The boatis approximately 300 yards fromthe base of the cliff.What is theangle of depression,to the nearestdegree,of the line of sight to theboat?  \n8.  At 10:00am,a person observes a hot air balloon climbing vertically in the air from apoint 300 meters away from the launch pad for the balloon.The angle of elevation tothe top of the balloon at this time is 25°.At 10:02am,the person observes that theangle of elevation to the balloon is now 60°.What is the change in altitude,to thenearest meter,for the balloon over the 2 minutes between the first and secondobservations?  \n300  \nKex  \n# Angle of Elevation and Angle of Depression\n\nExample 1  \n   \nAt a point on the ground 40 feet from the foot of a tree,the angle of elevation of the top ofthe tree is 42°.Find the height of the tree,to the nearest te  \nfeet3.0=× an2=Xta收  \nExample 2  \n   \nFind,to the nearest degree,the angle of elevation of the sun when a vertical post 15 feet highcasts a shadow which is 20 feet long.  \n37 =tan—1()ta  \n37°  \nExample 3  \n   \nAn observer in a balloon,which is 2000 feet above an airport,finds that the angle of  \ndepression of a steamer ship out at sea is 21 degrees.Find,to the nearest hundred feet,thedistance between the observer in the balloon and the steamer ship at sea.  \nExample 4  \n   \nFrom the top of a lighthouse 160 feet high,the angle of depression of a boat out at sea is 24°.Find,to the nearest foot,the distance from the boat to the foot of the lighthouse.(The footof the lighthouse is at sea level.)  \nExample ","cbCaibjfxXkzxkqL","https://ap.wps.com/l/cbCaibjfxXkzxkqL","pdf",319552,"English","# Example Problems\n## Practice /Homework","[{\"question\":\"How do you find a tree’s height from an angle of elevation and a horizontal distance?\",\"answer\":\"Use the given horizontal distance and the angle of elevation to form a right triangle, then apply a trigonometric function (typically tangent) to solve for height, rounding as instructed.\"},{\"question\":\"What is an angle of depression and how is it used to find distances to an object below?\",\"answer\":\"Angle of depression is measured from a higher viewpoint down to a lower object. You pair the angle with the horizontal distance or use relationships from a right triangle to compute the required distance, rounding to the specified unit.\"},{\"question\":\"Why do these problems specify different rounding targets such as the nearest degree or nearest foot?\",\"answer\":\"Each problem requires a particular precision for the final answer. The rounding rule ensures the distance or angle is reported in the correct level of accuracy requested by the question.\"}]","Angle of Elevation and Angle of Depression - Examples and Practice | PDF",1790046566]