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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 12
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.)
A plane is flying at an altitude of 2000 m. The angle of depression to a point on the ground is 45°. What is the horizontal distance from the plane to the point?
A ramp is inclined at 30° to the horizontal. If the ramp is 5 m long, what is the vertical height it reaches? (Give your answer to 2 decimal places.)
A ship sails 8 km east and then 6 km north. How far is the ship from the starting point?
A surveyor measures the angle of elevation to the top of a hill as 25°. If the surveyor is 100 m from the 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 30°. What is the height of the tree? (Give your answer to 2 decimal places.)
A triangle has angles 30°, 60°, and 90°. If the side opposite the 30° angle is 5 cm, what is the length of the hypotenuse?
Explain how trigonometry is used in navigation.
If sin θ = 0.6 and θ is an acute angle, what is the value of cos θ?
If the angle of elevation to the top of a building is 45° and you are standing 50 m away from the base, what is the height of the building?
If the sides of a triangle are 7 cm, 24 cm, and 25 cm, what is the measure of the largest angle?
The angle of depression from the top of a tower 50 m high to a point on the ground is 30°. Find the distance from the base of the tower to the point. (Give your answer to 2 decimal places.)
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?
Which trigonometric ratio is used to find the length of the side opposite a given angle in a right triangle when the hypotenuse is known?
A 20 m tall vertical pole stands on a slope that makes an angle of 12° with the horizontal. What is the angle of elevation from a point 30 m downhill from the base of the pole to the top of the pole? (Give your answer to 2 decimal places.)