Question

ART D: THINKING

17
Solve for x in the following diagram. Make sure to show all your work and clearly label your
diagram with any missing information.
E
65
PP
55°
Y
ye
52 m
70°
1151
А
B
Ads
***

Answer 1

110.41m

Explanation:

To get the value f x, we need to use SOH, CAH, TOA identity on ΔAEB but first we need to know any of the sides EB or AB.

From ΔBED, sum of the the angle in the triangle is 180° i.e ∠BED+∠EDB+∠EBD = 180°

65+55+∠EBD = 180

∠EBD = 180-120

∠EBD = 60

Also ∠DBC = 90- ∠EBD

∠DBC = 90- 60

∠DBC = 30°

Applying sine rule on ΔBCD;

52/sin∠DBC = DB/sin115

52/sin30 = DB/sin115

DB = 52sin115/sin30

DB = 52sin115/0.5

DB = 104sin115

DB = 114.75 m

Also applying sine rule on ΔBED to get side BE;

BE/sin55 = 114.75/sin65

BEsin65 = 114.75sin55

BE = 114.75sin55/sin65

BE = 93.998/0.906

BE = 103.75m

Finally, applying the trigonometry identity SOH on ΔABE

sinΔEAB = opp/hyp

sin70° = BE/AE

Since AE = x;

sin70° = 103.75/x

x = 103.75/sin70°

x = 110.41m

Hence, the value of x missing is approximately 110.41m