Gr12 Mathematics: Ch 4.4 Application of Trigonometric Functions

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Questions and Answers

What is the formula for the height of a pole?

  • $h = rac{d \sin \alpha}{\sin eta} an eta$ (correct)
  • $h = d \cos \alpha$
  • $h = d an \alpha$
  • $h = rac{d \sin eta}{\sin \alpha}$

In triangle FAB, what is the relation between FB and d?

  • FB = d
  • FB = d $\sin \alpha$
  • FB = d $\cos \alpha$
  • FB = $rac{d \sin \alpha}{\sin eta}$ (correct)

What is the formula for the height of a building?

  • $h = b \cos \alpha$
  • $h = rac{b \sin \alpha \sin heta}{\sin(eta + heta)}$ (correct)
  • $h = b \sin \alpha$
  • $h = rac{b \cos \alpha}{\sin heta}$

In triangle BCD, what is the relation between BD and b?

<p>BD = $rac{b \sin heta}{\sin(eta + heta)}$ (B)</p> Signup and view all the answers

In which triangle is the sine rule used to find the height of a building?

<p>Both triangles ABD and BCD (C)</p> Signup and view all the answers

What is the formula to find the area of a triangle ABC?

<p>$rac{1}{2}ab \sin C$ (D)</p> Signup and view all the answers

When to use the Sine Rule?

<p>When two angles and a side are given, but not the included angle (B)</p> Signup and view all the answers

What is the formula to find the side length 'a' using the Cosine Rule?

<p>$a^2 = b^2 + c^2 - 2bc \cos A$ (B)</p> Signup and view all the answers

What is the first step in solving problems in three dimensions?

<p>Draw a sketch using the given information (D)</p> Signup and view all the answers

When to use the Area Rule?

<p>When no perpendicular height is given (D)</p> Signup and view all the answers

What is the formula to find the side length 'b' using the Cosine Rule?

<p>$b^2 = a^2 + c^2 - 2ac \cos B$ (A)</p> Signup and view all the answers

In triangle FAB, what is the value of FB in terms of d, alpha and beta?

<p>FB = d sin alpha / sin beta (B)</p> Signup and view all the answers

What is the value of h in terms of b, alpha, beta and theta for the height of a building?

<p>h = b sin alpha / sin(beta + theta) (A)</p> Signup and view all the answers

In which triangle is the tangent ratio used to find the height of a pole?

<p>Triangle TFB (A)</p> Signup and view all the answers

What is the common angle used in both triangles FAB and TFB for the height of a pole?

<p>Beta (B)</p> Signup and view all the answers

What is the given angle in triangle TFB for the height of a pole?

<p>90 degrees (D)</p> Signup and view all the answers

What is the formula to find the area of a triangle when no perpendicular height is given?

<p>Area = 1/2 ac sin B (B)</p> Signup and view all the answers

In which situation would you use the cosine rule?

<p>When three sides are given (C), When two sides and the included angle are given (D)</p> Signup and view all the answers

What is the general approach to solving problems in three dimensions?

<p>Draw a sketch, consider the given information, apply appropriate rules, and calculate the desired quantities (D)</p> Signup and view all the answers

What is the formula to find the side length 'c' using the cosine rule?

<p>c^2 = a^2 + b^2 - 2ab cos C (D)</p> Signup and view all the answers

When would you use the sine rule?

<p>When no right angle is given, and either two angles and a side or two sides and an angle (not the included angle) are given (C)</p> Signup and view all the answers

What is the formula to find the area of a triangle when the base and height are given?

<p>Area = 1/2 bh (D)</p> Signup and view all the answers

In a three-dimensional problem, if FBA = and FBT = , what is the correct expression for FB in terms of d, , and ?

<p>$rac{d \sin \alpha}{\sin eta}$ (B)</p> Signup and view all the answers

In a three-dimensional problem, if BC = b, DBA = , DBC = , and DCB = , what is the correct expression for BD in terms of b, , and ?

<p>$rac{b \sin heta}{\sin(eta + heta)}$ (A)</p> Signup and view all the answers

In a three-dimensional problem, if FAB = and FBT = , what is the correct expression for h in terms of d, , and ?

<p>$d \sin \alpha an eta$ (D)</p> Signup and view all the answers

In a three-dimensional problem, if BC = b, DBA = , DBC = , and DCB = , what is the correct expression for h in terms of b, , , and ?

<p>$rac{b \sin \alpha \sin heta}{\sin(eta + heta)}$ (A)</p> Signup and view all the answers

In a three-dimensional problem, which trigonometric ratio is used to relate the height h to the distance FB in triangle TFB?

<p>Tangent Ratio (C)</p> Signup and view all the answers

In a triangle ABC, if a = 5, b = 7, and angle A is 30°, what is the length of side c?

<p>6.71 (D)</p> Signup and view all the answers

In a triangle PQR, if p = 9, q = 12, and angle Q is 45°, what is the area of the triangle?

<p>27 (A)</p> Signup and view all the answers

In a triangle DEF, if d = 10, e = 8, and angle E is 60°, what is the length of side f?

<p>12.16 (C)</p> Signup and view all the answers

Which of the following is NOT a step in solving problems in three dimensions?

<p>Use the Pythagorean theorem (D)</p> Signup and view all the answers

In a triangle GHI, if g = 11, i = 13, and angle G is 75°, what is the length of side h?

<p>17.14 (B)</p> Signup and view all the answers

Which of the following rules is used to find the area of a triangle when no perpendicular height is given?

<p>Area Rule (D)</p> Signup and view all the answers

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