Applications of Trigonometry
Math ⇒ Trigonometry
Applications of Trigonometry starts at 10 and continues till grade 12.
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See sample questions for grade 12
Explain how trigonometry is used in navigation.
Which formula is used to find the area of a triangle when two sides and the included angle are known?
Which trigonometric function relates the adjacent side and hypotenuse in a right triangle?
Which trigonometric ratio is used to find the height of a building when the angle of elevation and the distance from the building 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, find the height of the building. (Give your answer to 2 decimal places.)
A flagpole is 12 m high. The angle of elevation from a point on the ground to the top of the flagpole is 40°. How far is the point from the base of the flagpole? (Give your answer to 2 decimal places.)
A ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m from the wall, how high up the wall does the ladder reach? (Give your answer to 2 decimal places.)
A person observes the top of a tower at an angle of elevation of 60°. If the person is standing 20 m from the base, what is the height of the tower? (Give your answer to 2 decimal places.)
Which of the following is NOT a trigonometric application in real life? (1) Surveying land (2) Calculating time zones (3) Engineering design (4) Satellite navigation
Which of the following is NOT an application of trigonometry? (1) Measuring heights of mountains (2) Calculating distances in astronomy (3) Determining chemical formulas (4) Navigation
Which of the following is the correct Law of Cosines? (1) c² = a² + b² - 2ab cos C (2) c² = a² + b² + 2ab cos C (3) c² = a² - b² + 2ab cos C (4) c² = a² + b² - ab cos C
Which of the following is the correct Law of Sines? (1) a/sin A = b/sin B = c/sin C (2) a/sin B = b/sin C = c/sin A (3) a/sin C = b/sin A = c/sin B (4) a/sin A = b/sin C = c/sin B
Fill in the blank: The ______ of depression is the angle formed by the line of sight below the horizontal when looking down at an object.
Fill in the blank: The angle of ______ is the angle formed by the line of sight above the horizontal when looking up at an object.
Fill in the blank: The Law of Cosines is used to find the ______ of a triangle when two sides and the included angle are known.
Fill in the blank: The Law of Cosines is especially useful for finding the ______ of a triangle when all three sides are known.
A triangle has sides of length 8 cm, 15 cm, and 17 cm. Is this triangle a right triangle?
True or False: The Law of Cosines reduces to the Pythagorean theorem when the included angle is 90°.
True or False: The Law of Sines can be used to solve any triangle, including right-angled triangles.
True or False: The Law of Sines can be used to solve for unknown sides in a triangle when two angles and one side are known.
