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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 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)
A person observes the top of a building at an angle of elevation of 60°. If the person is standing 20 m from the building, what is the height of the building? (tan 60° = 1.732)
A person standing 80 m from a tower observes the top of the tower at an angle of elevation of 37°. What is the height of the tower? (tan 37° = 0.753)
A person stands 100 m from the base of a tower and observes the top at an angle of elevation of 30°. What is the height of the tower? (tan 30° = 0.577)
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?
A ramp is 5 m long and rises to a height of 1.2 m. What is the angle of elevation of the ramp to the nearest degree?
A ship is sighted at a distance of 500 m from a lighthouse. The angle of depression from the top of the lighthouse to the ship is 30°. What is the height of the lighthouse? (Give your answer to 2 decimal places.)
A surveyor measures the angle of elevation to the top of a hill as 25° from a point 200 m from its base. What is the height of the hill? (Give your answer to 2 decimal places.)
A tree casts a shadow 15 m long when the angle of elevation of the sun is 45°. What is the height of the tree?
A triangle has sides of length 7 cm, 8 cm, and 9 cm. Use the cosine rule to find the angle opposite the side of length 9 cm. (Give your answer to the nearest degree.)
If sin θ = 0.6 and θ is an acute angle, what is the value of cos θ?
If the angle of depression from the top of a tower to a point on the ground is 30°, and the tower is 50 m high, how far is the point from the base of the tower? (Give your answer to 2 decimal places.)
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.