15.2.2 Trigonometry, PT3 Focus Practice


Question 6:
In diagram below, AEC and BCD are straight lines. E is the midpoint of AC.

Given cosx= 5 13  and siny= 3 5
(a) find the value of tan x.
(b) Calculate the length, in cm, of BD.

Solution:

(a) Given cos x= 5 13 , therefore BC=5, AB=13 AC= 13 2 5 2  = 16925  = 144  =12 cm tan x= AC BC = 12 5


(b) For ΔDCE: siny= 3 5 EC DE = 3 5 EC 10 = 3 5 EC= 3 5 ×10=6 cm D C 2 = 10 2 6 2    =64   DC=8 cm For ΔABC: AC=2×6=12 cm tanx= 12 5 12 CB = 12 5 CB=5 cm BD=DC+CB =8 cm + 5 cm =13 cm



Question 7:
In diagram below, T is the midpoint of the line PR.

(a) Find the value of tan xo.
(b) Calculate the length, in cm, of PQ.

Solution:
(a) T R 2 = 13 2 12 2   =169144   =25 TR= 25  =5 cm tan x o = 12 5

(b) PR=2×5 cm  =10 cm P Q 2 = 10 2 8 2    =10064    =36 PQ= 36  =6 cm

Question 8:
In diagram below, ABE and DBC are two right-angled triangles ABC and DEB are straight lines.


It is given that cos y o = 3 5 .
(a) Find the value of tan xo.
(b) Calculate the length, in cm, of DE.

Solution:
(a) tan x o = 7 24

(b) cos y o = BC 20    3 5 = BC 20 BC= 3 5 ×20  =12 cm B D 2 = 20 2 12 2   =400144   =256 BD= 256  =16 cm DE=167   =9 cm

Question 9:
Diagram below shows a vertical pole, PQ. At 2.30 p.m. and 5.00 p.m., the shadow of the pole falls on QR and QS respectively.
Calculate
(a) the height, in m, of the pole.
(b) the value of w.

Solution:
(a)
tan  55 o = Height of the pole 3.2 Height of the pole=tan  55 o ×3.2 =1.428×3.2 =4.57 m

(b)
tan w= 4.57 3.20+2  = 4.57 5.20  =0.879    w= 41 o 18


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