Trigonometric Ratios

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) … Read more

Question 7: 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  = 169−25  = 144  =12 cm … Read more

Question 4: In the diagram, PQR and QTS are straight lines. It is given that tany= 3 4 , calculate the length, in cm, of RS. Solution: In △ PQT, tany= PQ QT 3 4 = 6 QT QT=6× 4 3  =8 cm In △QRS, QS=8+8=16 cm ∴R S 2 = 12 2 + 16 2 ←   pythagoras’ Theorem     =144+256   =400 RS= … Read more

5.2.1 Trigonometric Ratios, PT3 Focus Practice Question 1: Diagram below shows a right-angled triangle ABC. It is given that  cos x o = 5 13 , calculate the length, in cm, of AB. Solution: cos x o = AB AC cos x o = 5 13 AB 39 = 5 13 AB= 5 13 ×39 … Read more

5.1.2  Values of Tangent, Sine and Cosine 1.   The values of the trigonometric ratios of 30o, 45o and 60o (special angle) are as below.   2.   1 degree is equal to 60 minutes. 1o= 60’ 3.   A scientific calculator can be used to find the value of the sine, cosine or tangent … Read more

5.1 Trigonometric Ratios   5.1.1 Trigonometrical Ratios of an Acute Angle 1.     2.   Hypotenuse is the longest side of the right-angled triangle which is opposite the right angle. 3.   Adjacent side is the side, other than the hypotenuse, which has direct contact with the given angle, θ. 4.   Opposite side is the side … Read more