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

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