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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. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
See sample questions for grade 10
A plane is flying at a height of 1200 m. The angle of depression to a point on the ground is 45°. How far is the point from the plane horizontally?
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 communication tower is supported by a wire anchored to the ground at a point 24 m from the base of the tower. If the wire makes an angle of 72° with the ground, calculate the length of the wire to the nearest meter.
A mountain is observed from two points A and B, which are 500 m apart on a straight line passing through the base of the mountain. The angles of elevation of the top of the mountain from A and B are 30° and 45°, respectively. Find the height of the mountain to the nearest meter.
A river is 80 m wide. A tree on one bank is observed from a point on the opposite bank at an angle of elevation of 40°. If the observer’s eye level is 1.5 m above the ground, find the height of the tree to the nearest meter.
A ship is sailing due north. At a certain point, the angle of elevation of the sun is 60°. After sailing 500 m further north, the angle of elevation becomes 45°. Assuming the sun’s altitude remains constant, calculate the height of the sun above the sea level to the nearest meter.
A tower stands on a horizontal plane. From a point 50 m from the base of the tower, the angle of elevation to the top is 35°. From a point 30 m further away from the first point, the angle of elevation is 25°. Find the height of the tower to the nearest meter.
A vertical pole and a vertical building are 40 m apart. The angle of elevation from the top of the pole to the top of the building is 28°. If the pole is 18 m high, find the height of the building to the nearest meter.
In triangle ABC, AB = 12 cm, AC = 9 cm, and angle BAC = 120°. Find the length of side BC to two decimal places.