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Trigonometry of right angle triangle

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Added on  2021-02-20

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Trigonometry TABLE OF CONTENTS TASK 11 AC 1.11 AC 1.23 TASK 23 AC 2.13 AC 2.24 AC 2.36 AC 2.48 AC 3.1, 3.2 8 TASK 39 AC 4.1, 4.2 9 AC 5.110 AC 5.211 TASK 1 1 AC 1.1 1.) cos x = 9/41 In the triangle xyz: xz = 41 xy= 9 Solution cos x = base of the triangle / Hypotenuse of right angle triangle Thus,

Trigonometry of right angle triangle

   Added on 2021-02-20

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Trigonometry
Trigonometry of right angle triangle_1
TABLE OF CONTENTSTASK 1............................................................................................................................................1AC 1.1..........................................................................................................................................1AC 1.2..........................................................................................................................................3TASK 2............................................................................................................................................3AC 2.1 .........................................................................................................................................3AC 2.2..........................................................................................................................................4AC 2.3..........................................................................................................................................6AC 2.4 .........................................................................................................................................8AC 3.1, 3.2...................................................................................................................................8TASK 3............................................................................................................................................9AC 4.1, 4.2...................................................................................................................................9AC 5.1 .......................................................................................................................................10AC 5.2 .......................................................................................................................................11
Trigonometry of right angle triangle_2
TASK 1AC 1.11.)cos x = 9/41 In the triangle xyz: xz = 41xy= 9Solutioncos x = base of the triangle / Hypotenuse of right angle triangle Thus, from the given value of cos x it can be observed that: Base (B) = 9Hypotenuse (H) = 41Perpendicular (P) = √ (41)² - (9)² = 40Sin x = P/H = 40/41 tan x = P/B = 40/9 cosec x = 1/sinx = H/P = 41/40 sec x = 1/ cos x = H/B = 41/9 cot x = 1/ tan x = B/P = 9/402.)sin θ = 0.625 cos θ = 0.5 Solutioncosec θ = 1/sin θ = 1/0.625 = 1.6 sec θ = 1/cos θ = 1/0.5 = 2Using the identity: 1+tan² θ = sec² θ The value of tan θ = 1.73 cot θ = 1/tanθ = 1/1.73 = 0.573.)Angle of depression = 30°Height of cliff = 75 m 1
Trigonometry of right angle triangle_3
After 1 minute (60 seconds): Angle of depression = 20°Solution Let the intitial position of ship is at point C and final position at point D. Alternate angles between parallel lines are equal. Thus, angle ACB = 30° and angle ADB = 20° From the figure it can be observed that AB = 75 Tan 30 = AB/BC = 75/BCSo BC = 129.9 m, which represents the first position of the ship Similarly, Tan 20 = AB / (BC +CD) On substituting values we get: 129.9 + CD = tan 20CD = 76.16 m Thus, in one minute (60 seconds) ship sails a distance of 76.16 m Hence, Speed = distance /time = 76.16/60 = 1.26 m/sec Speed = 4.57 km/hour 2
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