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Applications of Trig
FunctionsEQ: How do I use trigonometry
in real-life application problems?
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Angles of Elevation and
Depression
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4. A closed circuit television camera ismounted on a wall .4 feet above a security
des! in an office building. It is used to viewan entrance door ".# feet from t$e des!.
%ind t$e angle of depression from t$e
camera lens to t$e entrance door.
.4 feet
?
?
".# feet
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&. '$e world(s longest escalator is t$e)eningrad *nderground in )enin +,uare. '$e
escalator $as an angle of elevation of .#/0and a vertical rise of "&.1 ft. %ind t$e
lengt$ of t$e escalator.
"&.1 feet
.#/0
?
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/. %ind t$e $eig$t of a flagpole w$ic$
casts a s$adow of ".#2 m w$en t$e sun
ma!es and angle of /#to t$e $ori3ontal.
9.32 m
63
63
?
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. A train must climb at a constantgradient of &.& m for every 2 m of
trac!. %ind t$e angle of incline.
200m5.5 m
?
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1. %ind t$e pitc$ of t$e roof.
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Trigonometry and 3-DFigures
EQ: How do you findtrigonometric ratios to find
un!nown sides and angles in #-5figures?
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". In t$e triangular prism find 5% and
t$e angle A%5.
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. All edges of a s,uare-based pyramidare cm in lengt$. %ind t$e angle
between t$e slant edge and a basediagonal.
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. %ind t$e angle between Q6 and t$ebase of t$e #-5 figure.
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2. %ind t$e angle 78 ma!es wit$ Q8.
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#. A symmetric s,uare-based pyramid$as base lengt$s of /cm and $eig$t of1cm as s$own. %ind t$e measure of t$e
face 'Q9 and t$e base
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Areas of Triangles
EQ: How do you find t$e area ofa triangle using trigonometry?
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Review
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What happens if you dont
now the height!!!
'$ere are some cases w$ere you don(t
need t$e $eig$t to find t$e area
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What happens if you dont
now the height!!!
'$ere are some cases w$ere you don(t
need t$e $eig$t to find t$e area
;ou $ave two sides and t$e
included angle
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"a#eling a Triangle
If you $ave a triangle A
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Formula for the Area of a Triangle
when you have $ sides and the includedangle%
'$e area of triangle is $alf of t$eproduct of two sides and t$e sine oft$e included angle
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%ind t$e area of t$e triangle: