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Federal (FBISE) · Chapter test · Free

10th Class Mathematics Chapter 8 Test08. Application of Trigonometry

29 marks · 40 minutes · 20 questions. Covers: 08. Application of Trigonometry.

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10th Class Mathematics Chapter 8 Test

10th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 29Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 9 × 1 = 9)

  1. In right △ABC, a = 2 cm , c = 4 cm, what is α?
    1. 30°
    2. 45°
    3. 60°
    4. 120°
  2. For an equilateral triangle, r : r1 : R =
    1. 1: 2 : 3
    2. 3: 2 : 1
    3. 1: 1 : 2
    4. 1: 3 : 2
  3. If a , a and b are length sides of an isosceles triangle, then S = . . .
    1. a2+b\frac{a}{2} + b
    2. a+a+b2a + \frac{a +b}{2}
    3. a−a+b2a - \frac{a +b}{2}
    4. a+b2a + \frac{b}{2}
  4. Area of an equilateral triangle having side a is:
    1. 38a\frac{\sqrt{3}}{8}a
    2. 34a2\frac{\sqrt{3}}{4}a^2
    3. 316a2\frac{\sqrt{3}}{16}a^2
    4. 316a\frac{\sqrt{3}}{16}a
  5. If a = 5 , b = 10 , c = 20 are sides of a triangle ABC, then angle α is
    1. Not possible
    2. Acute
    3. Obtuse
    4. 0°
  6. Shadow of a man 5.6 ft tall is making an angle of elevation of 45∘ with the Sun. What is the length of shadow
    1. 2.8 ft
    2. 5.6 ft
    3. 8.4 ft
    4. 11.2 ft
  7. If in a triangle ABC, a = b = c, then tanα2tan \frac{\alpha}{2}= . . .
    1. S−aa\sqrt{\frac{S-a}{a}}
    2. S−bb\sqrt{\frac{S-b}{b}}
    3. S−cc\sqrt{\frac{S-c}{c}}
    4. All of these
  8. If in a triangle, a = 10 , b = 15 , α = 32∘, then β =
    1. 42.5°
    2. 46.5°
    3. 52.7°
    4. 62.8°
  9. Radius of circum-circle R = . . .
    1. a) a2sec⁡α2\frac{a}{2} \sec \frac{\alpha}{2}
    2. a) b2sec⁡β2\frac{b}{2} \sec \frac{\beta}{2}
    3. a) c2csc⁡γ2\frac{c}{2} \csc\frac{\gamma}{2}
    4. a) c2cos⁡γ2\frac{c}{2} \cos \frac{\gamma}{2}

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Prove that r2=4Rcos⁡α2cos⁡γ2sin⁡β2 r_2 = 4R \cos \frac{\alpha}{2} \cos \frac{\gamma}{2} \sin \frac{\beta}{2}
  2. Find the area of triangular region ABC in the following. a = 8 , b = 14 , γ = 68.7°
  3. If cos⁡θ = 0.559, find the values of sin (180°− θ)
  4. Solve by using the Law of Tangents. a = 7 , b = 10 , c = 12
  5. Solve right-angled triangles ABC in which γ = 90° and c = 30 cm , a = 40 cm
  6. Solve the following oblique triangles a = 44 , b = 33 , c = 55
  7. Solve the right triangle ABC in which γ = 90⁰ , a = 5 cm , c = 13 cm
  8. Use the Law of Cosines to find the remaining side(s) and angle(s) in triangle ABC a = 150 , c = 150 , β = 15⁰

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. Show that:4Rcos⁡α2cos⁡β2cos⁡γ2=r2cot⁡α2cot⁡β2cot⁡γ2=Δ 4R \cos \frac{\alpha}{2} \cos \frac{\beta}{2} \cos \frac{\gamma}{2} = r^2 \cot \frac{\alpha}{2} \cot \frac{\beta}{2} \cot \frac{\gamma}{2} = \Delta
  2. A geologist wants to measure the diameter of a crater. From her camp, it is 4 miles to the northern-most point of the crater and 2 miles to the southern-most point. If the angle between the two lines of sight is 117°, what is the diameter of the crater?
  3. Solve by using appropriate law. c = 88 , β = 23.2⁰ , γ = 73⁰14'