Question #deeb3

2 Answers
Oct 14, 2016

Drawn

In figure
AB = h ft = Height of the building
C is the point on the ground from which angle of elevation of building #/_ACB=30^@20'=(30+20/60)^@=(91/3)^@#

D is the point on the ground(50 ft closer to the building from C) from which angle of elevation of building #/_ADB=45^@#
Let BD = x ft

Now #(AB)/(BD)=h/x=tan/_ADB=tan45^@=1#

#=>h/x=1=>x=h#

Again#(AB)/(BC)=(AB)/(BD+DC)=h/(x+50)=tan/_ACB=tan(91/3)^@#

#=>h/(x+50)=0.585#

#=>h/(h+50)=0.585#

#=>h=(h+50)xx0.585#

#=>h(1-0.585)=50xx0.585~~29.25#

#h=29.25/0.415~~70.5 ft#

Feb 5, 2017

Height of building#=70.5ft#

Explanation:

Let line AB be the building with A the top.
Let C be the first point with ascending angle 30°20'
Let D be the second point with ascending angle 45°

In triangle ACD #angle D = 180°-45°=135°#

#:.180°-(135°+30°20')=14°40'= angle A#

In triangle ACD:

#(AD)/(Sin30°20')=50/(sin14°40')#

Multiply both sides by #sin30°20'#

#:.cancel(sin30°20')/1 xx ( AD)/cancel(sin30°20')=(50 xx sin30°20')/(sin14°40')#

#:.AD=(50 xx 0.505029841)/(0.253195168)#

#:.AD=(25.25149208)/(0.253195168)#

#:.AD=99.73133484=hypotenuse#

In triangle ADB #angle D = 45°#

AB=height of building=opposite side

#:.sin45°=(opposite)/(hypotenuse)#

#:.AB=sin45 xx 99.73133484#

#:.AB=70.5ft#