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Chun Hei asked in 科學及數學數學 · 1 decade ago

maths question

1.cos30度xcos45度+sin60度xsin45度

2. cos^2 45度xsin30度

_________________

tan^2 60度

3. tan60度 = 開方8xcos45度

_______

sin(acute angle/3+35度)

4.BCDE is a triangle and ABC is a straight line. If Ad is 20cm,AE =10x開方2and ADE=60度,find the lenght of CD and cx

1 Answer

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  • 1 decade ago
    Favorite Answer

    (I omitted the degree notation)

    sqrt. denotes square root.

    (1)

    (cos 30)(cos 45)+(sin 60)(sin 45)

    =(2 sqrt.)/2[2 cos 30]

    =(2 sqrt.)cos 30

    =(2 sqrt.)(3 sqrt./2)

    =6 sqrt./2

    (2)

    (cos²45)(sin 30)/tan²60

    =(2 sqrt./2)²(1/2)/(3 sqrt.)²

    =(1/2)(1/2)/3

    =1/12

    (3)

    tan 60/sin (θ/3+35)=8 sqrt. cos 45

    3 sqrt./sin (θ/3+35)=2(2 sqrt.)(2 sqrt.)/2

    3 sqrt./sin (θ/3+35)=2

    sin (θ/3+35)=3 sqrt./2

    Because θ is an acute angle, therefore there is only one solution for θ/3+35

    θ/3+35=60

    θ/3=25

    θ=75

    (4)

    Is there a figure?

    I think it is not showing clearly.

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