Higher Engineering Mathematics, Sixth Edition

106 Higher Engineering Mathematics

Area of triangleXYZ

=^12 (base) (perpendicular height)

=^12 (XY)(XZ)=^12 ( 18. 37 )( 7. 906 )

=72.62mm^2

Now try the following exercise

Exercise 47 Further problems on the

solution of right-angled triangles

1. Solve triangleABCin Fig. 11.17(i).
   [
   BC= 3 .50cm,AB= 6 .10cm,
   ∠B= 55 ◦

]

(i)

B

AC5.0 cm

358

(iii)

418

G

l

H

15.0 mm

(ii)

F

E

D

3 cm

4 cm

Figure 11.17

2. Solve triangleDEFin Fig. 11.17(ii).
   [FE=5cm,∠E= 53 ◦ 8 ′,∠F= 36 ◦ 52 ′]


3. Solve triangle[ GHIin Fig. 11.17(iii).
   GH= 9 .841mm,GI= 11 .32mm,
   ∠H= 49 ◦

]

4. Solve the triangleJKLin Fig. 11.18(i)and find
   its area.

[

KL= 5 .43cm,JL= 8 .62cm,

∠J= 39 ◦,area= 18 .19cm^2

]

5. Solve the triangleMNOin Fig. 11.18(ii) and
   find its area.[
   MN= 28 .86mm,NO= 13 .82mm,
   ∠O= 64 ◦ 25 ′,area= 199 .4mm^2

]

(i)

518

J

KL

6.7 cm

(ii)

M

N

O

32.0 mm

258359

(iii)

P

8.75 m

3.69 mQ

R

Figure 11.18

6. Solve the trianglePQRin Fig. 11.18(iii) and
   find its area.[
   PR= 7 .934m,∠Q= 65 ◦ 3 ′,
   ∠R= 24 ◦ 57 ′,area = 14 .64m^2

]

7. A ladder rests against the top of the perpendi-
   cular wall of a building and makes an angle of
   73 ◦with the ground. If the foot of the ladder is
   2m from the wall, calculate the height of the
   building. [6.54m]

11.6 Angles of elevation and depression

(a) If, in Fig. 11.19,BCrepresents horizontal gro-

und andABa vertical flagpole, then theangle of

elevationof the top of the flagpole,A, from the

pointCis the angle that the imaginary straight

lineACmust be raised (or elevated) from the

horizontalCB,i.e.angleθ.

A

C B



Figure 11.19

(b) If, in Fig. 11.20,PQrepresents a vertical cliff and

Ra ship at sea, then theangle of depressionof

the ship from pointPis the angle through which

the imaginary straight linePRmust be lowered

(or depressed) from the horizontal to the ship, i.e.

angleφ.

P

Q R



Figure 11.20

(Note,∠PRQis alsoφ—alternate angles between

parallel lines.)

Problem 24. An electricity pylon stands on

horizontal ground. At a point 80m from the base of

the pylon, the angle of elevation of the top of the

pylon is 23◦. Calculate the height of the pylon to the

nearest metre.

Figure 11.21 shows the pylonAB and the angle of

elevation ofAfrom pointCis 23◦

tan23◦=

AB

BC

=

AB

80