subject

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 11
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)?
A radio tower is supported by a wire anchored 50 meters from its base. If the wire makes an angle of 60° with the ground, how high is the tower? (Round to the nearest meter.)
A ship sails 10 km east, then 24 km north. How far is the ship from its starting point?
A surveyor measures the angle of elevation to the top of a tower as 37°. Standing 80 meters from the base, how tall is the tower? (Round to the nearest meter.)
A tree casts a shadow 15 meters long when the angle of elevation of the sun is 45°. What is the height of the tree?
A triangle has sides a = 5 cm, b = 7 cm, and angle C = 60°. Find the length of side c (to two decimal places).
A triangle has sides of length 7 cm, 8 cm, and 9 cm. Find the largest angle of the triangle (to the nearest degree).
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.
If sin θ = 0.6 and θ is an acute angle, what is the value of cos θ?
The angle of depression from the top of a lighthouse to a boat is 30°. If the lighthouse is 50 meters high, how far is the boat from the base of the lighthouse?
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 communications tower is located on the top of a hill. From a point 400 meters from the base of the hill, the angle of elevation to the top of the hill is 20°, and to the top of the tower is 35°. Find the height of the tower to the nearest meter.
A mountain is observed from two points A and B, which are 500 meters apart on a straight line leading directly to the mountain. The angles of elevation to the top of the mountain from A and B are 30° and 45°, respectively. Calculate the height of the mountain to the nearest meter.
A navigation officer on a ship observes a lighthouse at a bearing of 045°. After sailing 5 km due east, the bearing to the lighthouse is now 330°. Calculate the distance from the second position to the lighthouse, to the nearest tenth of a kilometer.