Gr12 Mathematics: Ch 4.4 Application of Trigonometric Functions

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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?

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

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

Both triangles ABD and BCD Signup and view all the answers

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

$rac{1}{2}ab \sin C$ Signup and view all the answers

When to use the Sine Rule?

When two angles and a side are given, but not the included angle Signup and view all the answers

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

$a^2 = b^2 + c^2 - 2bc \cos A$ Signup and view all the answers

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

Draw a sketch using the given information Signup and view all the answers

When to use the Area Rule?

When no perpendicular height is given Signup and view all the answers

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

$b^2 = a^2 + c^2 - 2ac \cos B$ Signup and view all the answers

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

FB = d sin alpha / sin beta 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?

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

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

Triangle TFB Signup and view all the answers

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

Beta Signup and view all the answers

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

90 degrees Signup and view all the answers

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

Area = 1/2 ac sin B Signup and view all the answers

In which situation would you use the cosine rule?

When three sides are given Signup and view all the answers

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

Draw a sketch, consider the given information, apply appropriate rules, and calculate the desired quantities Signup and view all the answers

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

c^2 = a^2 + b^2 - 2ab cos C Signup and view all the answers

When would you use the sine rule?

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 Signup and view all the answers

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

Area = 1/2 bh 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 ?

$rac{d \sin \alpha}{\sin eta}$ 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 ?

$rac{b \sin heta}{\sin(eta + heta)}$ 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 ?

$d \sin \alpha an eta$ 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 ?

$rac{b \sin \alpha \sin heta}{\sin(eta + heta)}$ 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?

Tangent Ratio 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?

6.71 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?

27 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?

12.16 Signup and view all the answers

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

Use the Pythagorean theorem 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?

17.14 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?

Area Rule Signup and view all the answers