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  1. Asked: In:

    Given 15 cot A = 8, find sin A and sec A.

    girish08

    Given that: 15 cot A = 8 ⇒ cot A = 8/15 Let cot A = 8k/15k, where k is a real number. In ∆ ABC, by Pythagoras theorem, we have AC² = AB² + BC² = (8k)²+(15k)² = 64k²+225k² = 289k² ⇒ AC = √(289k²) = 17k Hence, sin A = BC/AC = 15k/17k = 15/17 and sec A = AC/AB = 17k/8k = 17/8 See here for video explanaRead more

    Given that: 15 cot A = 8
    ⇒ cot A = 8/15
    Let cot A = 8k/15k, where k is a real number.
    In ∆ ABC, by Pythagoras theorem, we have
    AC² = AB² + BC²
    = (8k)²+(15k)²
    = 64k²+225k²
    = 289k²
    ⇒ AC = √(289k²) = 17k
    Hence, sin A = BC/AC = 15k/17k = 15/17 and sec A = AC/AB = 17k/8k = 17/8

    See here for video explanation of this question👇😊

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  2. Asked: In:

    If sin A = 3 /4, calculate cos A and tan A.

    girish08

    Given that: sin A = 3/4 Let sin A = 3k/4/, where k is a real number. In ∆ABC, by Pythagoras theorem, we have AB² = AC²-BC² = (4k)²-(3k)² = 16k²-9k² = 7k² ⇒ AB = √(7k²) = √7k Hence, cos A = AB/AC = √7k/4k = √7/4 and tan A = BC/AB = 3k/√7k = 3/√7 Here is the video explanation of this question😃👇

    Given that: sin A = 3/4
    Let sin A = 3k/4/, where k is a real number.
    In ∆ABC, by Pythagoras theorem, we have
    AB² = AC²-BC²
    = (4k)²-(3k)²
    = 16k²-9k²
    = 7k²
    ⇒ AB = √(7k²) = √7k
    Hence, cos A = AB/AC = √7k/4k = √7/4 and tan A = BC/AB = 3k/√7k = 3/√7

    Here is the video explanation of this question😃👇

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  3. Asked: In:

    Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b)

    girish08

    (i) A(2,3), B(4,1) Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²) Distance between A(2,3) and B(4,1) is given by AB = √((4-2)²+(1-3)²) = √(4+4) = √8 = 2√2 (ii) P(-5,7), Q(-1,3) Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²) Distance between P(-5,7) and Q(-1,3) is given by PQ = √((-1-(-5))²+(3-7)Read more

    (i) A(2,3), B(4,1)
    Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²)
    Distance between A(2,3) and B(4,1) is given by AB
    = √((4-2)²+(1-3)²) = √(4+4) = √8 = 2√2

    (ii) P(-5,7), Q(-1,3)
    Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²)
    Distance between P(-5,7) and Q(-1,3) is given by PQ
    = √((-1-(-5))²+(3-7)²) = √(16+16) = √32 = 4√2

    (iii) M(a,b), N(-a,-b)
    Using the distance formula: √((x₂-x₁)²+(y₂-y₁)²)
    Distance between M(a,b) and N(-a,-b) is given by MN
    = √(-a-(a))²+(-b-(-b))²) = √(4a²+4b²) = 2√(a²+b²)

    Here is the video explanation for this question 👇

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  4. Asked: In:

    Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

    girish08

    Here, P(0,0) and Q(36, 15), using distance formula √((x₂-x₁)²+(y₂-y₁)²) Distance between P(0,0) and Q(36, 15) is given by PQ = √((36-0)²+(15- 0)²) = √(1296 + 225) = √1521 = 39 Using the distance formula: √((x₂-x₁)²+(y₂-y₁)² we can find the distance between the two towns. See this video solution 😁

    Here, P(0,0) and Q(36, 15), using distance formula √((x₂-x₁)²+(y₂-y₁)²)
    Distance between P(0,0) and Q(36, 15) is given by PQ
    = √((36-0)²+(15- 0)²) = √(1296 + 225) = √1521 = 39
    Using the distance formula: √((x₂-x₁)²+(y₂-y₁)² we can find the distance between the two towns.

    See this video solution 😁

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  6. Asked: In:

    Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear.

    girish08

    Here, A(1,5), B(2, 3) and C(-2,-11). Using distance formula: √((x₂-x₁)²+(y₂-y₁)²) AB = √((2-1)²+(3-5)²) = √(1+4) = √5 BC = √((-2-2)²+(-11-3)²) = √(16+196) = √212 CA = √((1-(-2))²+(5-(-11))² = √(9+256) = √265 Here, AB+BC = √5+√212 ≠ √265 = AC Hence, the points A(1,5), B(2,3) and C(-2,-11) are not colRead more

    Here, A(1,5), B(2, 3) and C(-2,-11).
    Using distance formula: √((x₂-x₁)²+(y₂-y₁)²)
    AB = √((2-1)²+(3-5)²) = √(1+4) = √5
    BC = √((-2-2)²+(-11-3)²) = √(16+196) = √212
    CA = √((1-(-2))²+(5-(-11))² = √(9+256) = √265
    Here, AB+BC = √5+√212 ≠ √265 = AC
    Hence, the points A(1,5), B(2,3) and C(-2,-11) are not collinear.

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