Math 1316
2.5 Applications of Right Triangles
Bearing: Other applications of right triangles involve bearing, an important concept in
navigation. There are two methods for expressing a bearing. When a single angle is given, such
as 1640, it is implied that the bearing is measured in a clockwise direction fro due north.
Examples: The solutions are shown on the next page.
1. The bearing of point B from point C is 2540. The bearing of point A from point C is 3440. The
bearing of point A from point B is 320. If the distance from A to C is 780 meters, find the
distance from A to B.
2. Two ships leave a port at the same time. The first ship sails on a bearing of 320 at 16 knots
and the second on a bearing of 1220 at 24 knots. How far apart are they after 2.5 hours?
3. The bearing from point A to point B is S 550 E and from a point B to point C is N 350 E. If a
ship sails from A to B, a distance of 81 km, and from B to C, a distance of 74 km, how far is it
from A to C?
4. A ship leaves a pier on a bearing of S 620 E and travels for 75 km. It then turns around and
continues on a bearing N 280 E for 53 km. How far is the ship from the pier?
5. From a point A on the ground, the angle of elevation to the top of a tall building is 24.10.
From a point B, which is 600 feet closer to the building, the angle of elevation is measured to be
30.20. Find the height of the building.
6. A pilot measures the angles of depression to two ships to be 400 and 520. If the pilot is flying
at an elevation of 35,000 feet, find the distance between the two ships.
7. The angle of elevation from Lone Pine to the top of Mt. Whitney is 10050’. A man traveling 7
km from Lone Pine along a straight level road toward Mt. Whitney, finds the angle of elevation
to be 22040’. Find the height of the top of Mt.Whitney along the level road.
d., S
SoIUT:lb/t5
1
No""&e;
<C =-3ljr!: J..S'I"
«c
t: rof)
;)'S-'1 ~J73'o0.•..•=1f
So
.
0
<. 13 -=-:;Y::'3~
D
:: f.;{
5/1t if2°:::
0
780
c
C ::: _ '980
St« f;;l o
C
= II G S", (P?
50 -t~tJ-/s,t;o,.CL
:frt7ft-\.
(h.,,- t:IT>
A CP 13 Is 11(p(p/n azer»
I
I
I
I
I
<.c z;/~e:'32
D
:::'lo~
13~-L~L- ~t~ C9
c = J +107...
&:LCWt
1
~01"'nt
2
C?. -:= (;02..+
C
C
'/02-
= J3'bD f'lhtJ"O
-=
US;zoo
-r/,L Shif3J
,4r-.e...
J5J.~ ~ 1;(,f
/2C{.",-tlcop(
/h//t,;
AfAfr;
)'1
;;;~s
4r>
3
A~----!-7C
«[5 :: 35 + S-SO
= 'lob
0
lJiJ 1:h~Pgtt:~CfYf#lf'fA'l1-1kr/?/ft.t
J?~
o .:
".2.
C·
,+0"Z
b = J8/~t'l2.
b
J IJ. D31-
A
o
A..
Ta«30,1 ::: X
XTaA30r~
~
h,
h.
X -::::
'ZaA:> 0, i-
it.
7:.all ~ 'I,J :::
(#jtJ-/-
_
~6._._
;ccM30,?.
ra/l~Jj~ /
(joo+~vr
~ (Jo7::(MJ'I,
2.) - A,
J -;- ~r:;~'/, ~~ -::::.Jv
t-4-/),3&1 r'tl
6(:J(l-CC4/J;)1f~1~
A_
~a/),;)'1"1~
70/),Jt?F2
~~r:x:tLa"l:2'1~/
:;:::,f;..-- 7C0..2 fd,
~
<];.Cw], de; r ~
)Iv
~ G'ooTa~2'/,(-,. /
) - T3rL~,1
- /t,...
c;::'~/130r ~
1/S'1, 1If:.~
z: /;
lif- )ti?~r @:s;dte-1:it>//J1'lJ
/S
ql'fr",yfm~
//0'9, -; -+ea- ¢q//:
13
;t ::;2~3ijlj,CJ?
.t-
$~1'5
eft ~ 'I~9//, 33
Are -/f~T1IE3ii - P.~ 37'7':. 79 :::. It:3 (}(Q, B .;s;cu-c
'i}..d
0,
//rAre:
J
I
0
x
A
J,. r~/o~/-
X.-f f- -
Q,••.•
~-f9)
(r~/l..ffj¥c/s-t:JJz:
Xr:ortleFs}c/
~
A,
-I- 71J;'ILJoostJ I:::
t:
I
-1L tq'l (/:I ~ + 1Z'&l1o ""sz; I -::= h.,
']:Ot1.f:;;l'9tl'
-2
0
/
L
T TW'zj 0 SD .:::/'l."'-
.
h ran)t::,'"" $0/
_
Z-qll~°9'(7 /
lj:~/D~{;J/
ltfJ.-- Ea-/}/t;:?~e I)
l!
7zu: /e/":So I
/
T~/}/8' i!?6'01
-~o)
,
--==- ;(
Z"C?"]:RQ Clyt7/
