Lesson Worksheet: Angles of Elevation and Depression Mathematics • 11th Grade
In this worksheet, we will practice solving real-world problems that involve angles of elevation and depression using the tangent ratio.
In the given diagram of a ladder leaning against a wall, which of the following angles represents the ladder’s angle of elevation?
A palm tree 10.6 meters tall is observed from a point 12 meters away on the same horizontal plane as the base of the tree. Find the angle of elevation to the top of the palm tree giving the answer to the nearest minute.
Anthony stands 40 m from a building that is 25 m high. What is the angle of elevation from Anthony to the top of the building? Round your answer to the nearest degree.
A ladder is leaning against a vertical wall such that the top is 9 m above the ground and its base is 3 m from the bottom of the wall. Find the measure of the angle between the ladder and the ground. Give your answer to two decimal places.
A ladder is leaning against a wall where the upper end is 4 m from the ground. The angle of inclination of the ladder to the ground is . Find the horizontal distance between the base of the ladder and the wall giving the answer to two decimal places.
A truck traveled 1.2 km up a ramp that is inclined to the horizontal at an angle of . Find the height at which the truck stopped, giving the answer in meters to one decimal place.
A flag is hung 22 meters up a flagpole. As the flag is raised, the angle of elevation from a point 21 meters away from the base of the flagpole to the flag is . Find the increase in height of the flag giving the answer to two decimal places.
In the given diagram, Benjamin observes a buoy in the sea below him from a point 6 ft above a 45 ft cliff. He has been told that the perpendicular distance from the buoy to the base of the cliff is 60 ft. What is the angle of depression, in degrees, from Benjamin to the buoy? Give your solutions to two decimal places.
Daniel wants to find the height of a tower. He decides he needs to make a clinometer in order to measure the angle of elevation. He uses a straw, a protractor, some string, and a bit of Blu-Tack as a weight. Daniel stands at a perpendicular distance of 100 ft from the base of the tower and measures the angle on his clinometer to be , as seen in the diagram.
Work out the angle of elevation.
Given that Daniel’s eyeline is 6 ft from the ground, work out the height of the tower to the nearest foot.
In the given diagram, a 15 ft ladder is leaning against a wall with an angle of elevation of . How high up the wall would it reach? Give your answer to two decimal places.