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 11
Describe a real-life situation where the angle of depression is used.
Explain how the Law of Sines can be used to solve for an unknown side in a triangle.
Explain how trigonometry is used in navigation.
Explain why trigonometry is important in engineering.
A building and a tree are 30 meters apart. The angle of elevation to the top of the building from the top of the tree is 25°. If the tree is 10 meters tall, how tall is the building? (Round to the nearest meter.)
A ladder leans against a wall making an angle of 60° with the ground. If the foot of the ladder is 2 meters from the wall, how long is the ladder? (Give your answer to two decimal places.)
A person standing 40 meters from a building observes the top of the building at an angle of elevation of 53°. How tall is the building? (Round to the nearest meter.)
A plane is flying at an altitude of 3000 meters. The angle of depression from the plane to a point on the ground is 20°. How far is the point on the ground from the plane (horizontally)?
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 in astronomy (3) Determining the area of a rectangle (4) Navigation at sea
Which of the following is the correct sine rule? (1) a/sin A = b/sin B = c/sin C (2) a² = b² + c² - 2bc cos A (3) sin A = cos B (4) tan A = a/b
Which trigonometric function is used to calculate the angle of elevation when the height and distance from the object are known? (1) Sine (2) Cosine (3) Tangent (4) Secant
Fill in the blank: The ________ of a triangle is used to find the area when two sides and the included angle are known.
Fill in the blank: The ________ of a triangle relates the lengths of the sides to the cosine of one of its angles.
Fill in the blank: The ________ of elevation is the angle formed by the line of sight upward from a horizontal line.
Fill in the blank: The angle of ________ is the angle formed by the line of sight downward from a horizontal line.
True or False: The cosine rule can be used to find an angle in a triangle when all three sides are known.
True or False: The sine rule can be used to find an unknown side in any triangle, not just right-angled triangles.
True or False: The sine rule can be used to solve for an unknown angle when all three sides of a triangle are known.
True or False: The tangent of an angle in a right triangle is the ratio of the adjacent side to the opposite side.
