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Each example guides readers to draw and label triangles, isolate the relevant right triangle, apply sine and tangent ratios, and answer with approximate, checked results.",{"@graph":14,"@context":65},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/trigonometry-word-problems-step-by-step-right-triangle-applications/267006/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/trigonometry-word-problems-step-by-step-right-triangle-applications/267006.png","ImageObject",300,407,{"name":42,"@type":43},"8796093062539","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-24","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",16,{"@type":57,"mainEntity":58},"FAQPage",[59],{"name":60,"@type":61,"acceptedAnswer":62},"Why are angle of elevation and angle of depression treated as equal in some problems?","Question",{"text":63,"@type":64},"When the situation is modeled with parallel lines cut by a transversal, the corresponding alternate interior angles are congruent, so the angle of elevation can equal the angle of depression for the same line of sight.","Answer","https://schema.org",{"og:url":32,"og:type":67,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":69,"canonical":32},"index,follow",{"doc_id":71,"site_id":7},267006,1789413927,{"code":4,"msg":74,"data":75},"success",[76,80,84,87,92,97,102,107,112,115,119],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":77,"show_sort_weight":78,"slug":79},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":81,"show_sort_weight":82,"slug":83},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":85,"slug":86},70,"exam",{"id":88,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},5,"Comic",60,"comic",{"id":93,"doc_module":4,"doc_module_name":25,"category_name":94,"show_sort_weight":95,"slug":96},6,"Technology",50,"technology",{"id":98,"doc_module":4,"doc_module_name":25,"category_name":99,"show_sort_weight":100,"slug":101},7,"Healthcare",40,"healthcare",{"id":103,"doc_module":4,"doc_module_name":25,"category_name":104,"show_sort_weight":105,"slug":106},8,"Research & Report",30,"research-report",{"id":108,"doc_module":4,"doc_module_name":25,"category_name":109,"show_sort_weight":110,"slug":111},9,"Religion & Spirituality",20,"religion-spirituality",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":113,"show_sort_weight":110,"slug":114},"World Cup","world-cup",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":116,"slug":118},10,"Lifestyle","lifestyle",{"id":120,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":88,"slug":122},19,"General","general",{"code":4,"msg":74,"data":124},{"doc_id":71,"user_id":125,"nickname":42,"user_avatar":11,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":131,"language":132,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":12,"update_tm":72,"read_time":136},8796093062539,"# Trigonometry Word Problems\n\nApplications of Right Triangles and Trig Functions  \nd  \nIncludes angle of elevation and depression,examples,step-by-step solutions,and more..  \nDraw a picture  \nand  \nlabel the parts  \nIsolate the triangle  \nand  \nSolve  \nand  \nlabel the parts  \nand  \nsolve  \n## Trigonometry Word Problems\n\nExample:You fly a kite 4 feet off the ground with 300 feet of string.There is a 40 mile per hour wind,and the kite forms a 29°angle from the ground.How high is the kite (from the ground)?  \nAnswer the question!Since the triangle is 4 feet off the ground,we need to add 4'to determine the heightof the kite from the ground.  \nTherefore,the kite is approximately 149.4'from the ground.  \nExample:A cable is attached to a pole 10 meters high.If the other end is attachedto the ground 8 meters from the base of the pole.How long is the cable?  \nDraw a picture  \nIsolate the triangle  \n### Basic Steps:\n\n1)Draw a picture  \n2)Label the parts  \n3)Isolate the triangle  \n4)Solve  \n5)Answer the question  \nSince we have a right triangle---withan angle and hypotenuse--we canuse the sine function to find the\"opposite\"side.  \ny=300'(.485)=145.4'  \nExample:A diver stands on a diving board above 2 swimmers.The angle of depression from the diver to each swimmeris 30 and 45 degrees.  \nIf the swimmers are 6 feet apart,how high is the diving board?  \nStep 1:Draw a picture  \nStep 2:Determine the right triangle(s)  \nStep 3:Solve  \nStep 4:Check  \n2h=(x+6)tan(30)  \nxtan(45)=(x+6)tan(30)  \nThen,ifx=8.18....  \nx(1)=(x+6)(.577)  \nx=.577x+3.464  \n30-60-90 triangle...  \n.423x=3.464  \n8.18xN3=14.184  \nX  \nx=8.19 feet  \nExample:Two players stand on a basketball court.  \nThe angles of elevation from the foot of each player to the 10'high basket are40 and 50 degrees.How far apart are the players from each other?  \nStep 1:Sketch  \nStep 2:Identify triangles and label  \n10'  \nStep 3:Solve  \n=8.39  \n\n| Angle of Elevation vs.Angle of Depression   |\n| --- |\n\nRecognizing and identifying angle of elevation or angle of depression can be confusing.Perhaps,this example will clarify the differences..  \n   \nExample:An airplane is flying 4000 feet above the ground.If the angle of depression to the airport runway is 12degrees,how far is the airplane from the runway?(what is the \"ground distance?\")  \nStep 1:Draw a picture  \nairplane  \nStep 2:Label the parts  \nStep 3:Isolate the triangle  \nThe angle of depression (from the plane tothe runway)is 12 degrees..  \n   \n   \nTherefore the angle of elevation (from therunway to the plane)is also 12 degrees!  \n   \n   \nNOTE:From geometry theorems,\"if parallellines cut by a transversal,then alternateinterior angles are congruent\"...  \nStep 4:Solve  \nStep 5:Answer the question  \nThe \"ground distance\"of the plane to the runwayis approximately 18,818 feet  \n   \nNotice,the angle of depressionbegins at the airplane's horizon4000'  \n   \nExample:Describe the angles as they relate to the objects in the diagram  \nAngle 1:Angle of elevation from man to the plane  \nAngle 2:Angle of depression from man to animal  \nAngle 3:Angle of elevation from animal to man  \nAngle 4:Angle of depression from plane to man  \nExample:A blimp hovers 400 feet above a stadium.A fan is standing outside the stadium.To directly view the blimp,the fan looks up at an angle(of elevation)of 7 degrees.Approximately,how far from the stadium is the fan standing?  \nStep 1:Draw a diagram  \nStep 2:Extract the right triangle  \nStep 3:Solve  \nStep 4:Check for reasonableness  \nthe side opposite the 83 degreeangle is significantly largerthan the side opposite the7 degree angle..L  \nExample:The slope of a ramp is-  \nWhat is the angle of elevation of the ramp?  \n   \nExample:A regular pentagon inscribed in a circle has a perimeter 50.What is the radius of the circle?  \nStep 1:Draw a sketch and label  \nStep 3:Solve  \nStep 2:Extract the right triangle  \nTo find r,we use the  \nright triangle...  \n(approximately)  \nPerimeter=50,so each side is 10  \n5 triangles--360 degrees..each part is","cbCaiaW456cZsPlS","https://ap.wps.com/l/cbCaiaW456cZsPlS","pdf",1130737,23,"English","# Trigonometry Word Problems\n## Right Triangles and Trig Functions\n## Angle of Elevation vs. Angle of Depression\n## Example Applications\n## Basic Steps for Solving","[{\"question\":\"Why are angle of elevation and angle of depression treated as equal in some problems?\",\"answer\":\"When the situation is modeled with parallel lines cut by a transversal, the corresponding alternate interior angles are congruent, so the angle of elevation can equal the angle of depression for the same line of sight.\"}]","Trigonometry Word Problems - Step-by-Step Right Triangle Applications | PDF",58]