📐 Trigonometry: Angles of Elevation & Depression

Q1. A boat is heading towards a lighthouse, whose beacon light is 45 m above the water. The boat's crew measures the angle of elevation from the deck to be 30°. What is the ship's horizontal distance from the lighthouse? Round your answer to the nearest hundredth of a metre.

Q2. From a hot air balloon, Yvonne measures a 25° angle of depression to a landmark that is 515 m away horizontally. What is the balloon's vertical distance above the ground? Round your answer to the nearest hundredth of a metre.

Q3. From a hot air balloon, Dave measures a 39° angle of depression to a landmark that is 228 m away horizontally. What is the balloon's vertical distance above the ground? Round your answer to the nearest tenth of a metre.

Q4. From the observation deck of a skyscraper, Mike measures a 68° angle of depression to a ship in the harbour below. If the observation deck is 347 m high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a metre.

Q5. From the observation deck of a tower, Sarah measures a 72° angle of depression to a car on the road. If the observation deck is 350 m high, what is the horizontal distance from the base of the tower to the car? Round your answer to the nearest tenth of a metre.

Q6. From a hot air balloon, a pilot measures a 30° angle of depression to a landmark that is 444 m away horizontally. What is the balloon's vertical distance above the ground? Round your answer to the nearest tenth of a metre.

Q7. Dennis is flying a kite, holding his hands at a height of 1.5 m above the ground and letting out all the kite's string. He measures the angle of elevation from his hand to the tip of the kite to be 52°. If the string from the tip to his hand is 30 m long, how many metres in the air does the kite fly? Round your answer to the nearest hundredth of a metre.

Q8. Owen is flying a kite, holding his hands at a height of 1.2 m above the ground and letting out all the kite's string. He measures the angle of elevation from his hand to the tip of the kite to be 66°. If the string from the tip to his hand is 30 m long, how many metres in the air does the kite fly? Round your answer to the nearest hundredth of a metre.

Q9. A 120 m tall communications tower casts a shadow. If the angle of elevation from the tip of the shadow to the top of the tower is 45°, how far is the tip of the shadow from the base of the tower? Round your answer to the nearest metre.

Q10. A surveyor stands 2.5 km from the base of a hill and measures the angle of elevation to the summit as 8°. How tall is the hill? Round your answer to the nearest metre.

Q11. Alexander leans a 6 m ladder against a wall so that it forms an angle of 80° with the ground. How high up the wall does the ladder reach?

Q12. A rescue worker leans an 8.5 m ladder against a building so that it forms an angle of 69° with the ground. How high up the wall does the ladder reach?