Question #04430

2 Answers
Dec 11, 2017

Answer:

The viewing angle between the base and top of the castle wall from the person on the boat will be

#theta=beta-alpha=19.8^@-9.1^@=10.7^@#

Explanation:

Let the angle of elevation of the top of the cliff or base of the castle from the boat be #alpha# and the angle of elevation of the top of the castle from the boat be #beta#

Again the perpendicular distance of the boat from the castle or cliff is #200m#

Height of the top of castle wall is #32m+40m=72m#

Height of the base of castle wall or top of the cliff is #32m#

So #tan beta=72/200=0.36#

#=>beta=tan^-1(0.36)=19.8^@#

And #tan alpha=32/200=0.16#

#=>alpha=tan^-1(0.16)=9.1^@#

Hence the viewing angle between the base and top of the castle wall from the person on the boat will be

#theta=beta-alpha=19.8^@-9.1^@=10.7^@#

Dec 11, 2017

Answer:

#10^@42'31''# or #10.7^@#

Explanation:

Viewing #angle# between bottom of wall and level line to
the foot of the cliff:-# =32/200=tan theta=9^@5'25''#

Vertical height between the foot of the cliff and top of wall

#=40+32=72m#

Viewing #angle# between bottom of cliffl and level line to
the top of the wall:-# =72/200=tan theta=19^@47'56''#

#=#the viewing angle between the base and the top of
the castle wall :-

#(19^@47'56'')-(9^@5'25'')=10^@42'31''# or #10.7^@#