Applications of Trigonometry
Math ⇒ Trigonometry
Applications of Trigonometry starts at 10 and continues till grade 12.
QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Applications of Trigonometry.
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See sample questions for grade 10
Which trigonometric ratio is defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle?
Which trigonometric ratio is used to find the height of a building when the distance from the building and the angle of elevation are known?
A building and a tree are 30 m apart. The angle of elevation from the top of the tree to the top of the building is 20°. If the tree is 15 m high, how tall is the building? (Give your answer to 2 decimal places.)
A cable is attached from the top of a 25 m pole to the ground at a distance of 7 m from the base. What is the angle the cable makes with the ground? (Give your answer to the nearest degree.)
A flagpole is 20 m high. From a point on the ground, the angle of elevation to the top of the flagpole is 30°. How far is the point from the base of the flagpole? (Give your answer to 2 decimal places.)
A kite is flying at a height of 30 m. The string makes an angle of 60° with the ground. What is the length of the string? (Give your answer to 2 decimal places.)
A ladder 10 m long leans against a wall making an angle of 60° with the ground. How high up the wall does the ladder reach? (Give your answer to 2 decimal places.)
A man observes the top of a tower at an angle of elevation of 53°. If he is standing 40 m from the base, what is the height of the tower? (tan 53° = 1.327)
The sine rule is applicable in which of the following cases? (1) Only right-angled triangles (2) Only isosceles triangles (3) Any triangle (4) Only equilateral triangles
Which of the following is NOT a trigonometric ratio? (1) Sine (2) Cosine (3) Tangent (4) Secant (5) Gradient
Which of the following is NOT an application of trigonometry? (1) Measuring heights of mountains (2) Calculating distances between planets (3) Determining the area of a rectangle (4) Navigation at sea
Which of the following is the correct expression for tan θ in a right-angled triangle? (1) Opposite/Adjacent (2) Adjacent/Opposite (3) Hypotenuse/Opposite (4) Opposite/Hypotenuse
Fill in the blank: The ________ of a triangle is the longest side, opposite the right angle.
Fill in the blank: The ________ rule relates the lengths of the sides of a triangle to the cosines of its angles.
Fill in the blank: The angle of ________ is the angle formed by the line of sight with the horizontal when looking down at an object.
Fill in the blank: The angle of ________ is the angle formed by the line of sight with the horizontal when looking up at an object.
True or False: The cosine of an acute angle is always positive.
True or False: The cosine rule can be used to find an unknown side in any triangle if two sides and the included angle are known.
True or False: The sine of an obtuse angle is always negative.
True or False: The sine rule can be used to find an unknown angle if all three sides of a triangle are known.
