Inverse Trigonometric Worksheets Grade 11

1. sin⁻¹(1/2) = ?
2. Liam is an aerospace engineer designing a landing approach path for a small aircraft. The plane must descend from an altitude of 3500 feet to a runway that is 7000 feet away horizontally. The descent angle θ satisfies the equation 3 tan(θ) = 1.5. What angle θ, in degrees, should Liam use for the approach path? Use an inverse trigonometric function and express your answer to the nearest tenth of a degree.
3. A 20-foot ladder leans against a building, making an angle θ with the ground. If the base of the ladder is 8 feet from the building, find the measure of angle θ in degrees. Round your answer to the nearest whole number.

…and 3 more problems

1. Charlotte is designing a suspension bridge for a school project. The main cable of the bridge forms a parabolic curve, and at a certain point, the vertical distance from the road deck to the cable is 9 meters, while the horizontal distance from the lowest point of the cable to that point is 12 meters. To analyze the cable's tension, Charlotte needs to find the angle θ (in degrees) that the cable makes with the horizontal at that point, where θ satisfies the equation 2 sin(θ) = 3 cos(θ). Solve for θ, where 0° < θ < 90°. Express your answer to the nearest tenth of a degree.
2. Aroha is an aerospace engineer designing a satellite dish. The dish's cross-section is a parabola. To ensure optimal signal reception, the receiver must be placed at the focus. The depth of the dish is 12 meters, and the diameter is 40 meters. The angle θ that the line from the focus to the rim makes with the axis of symmetry satisfies the equation tan(θ) = (diameter) / (4 × depth). Using inverse trigonometric functions, what is the angle θ in degrees? Round your answer to the nearest tenth of a degree.
3. An engineer is designing a ramp for wheelchair access to a building. The ramp must rise 2.5 meters vertically over a horizontal distance of 10 meters. What angle should the ramp make with the horizontal ground to meet accessibility standards? Express your answer in degrees to one decimal place.

…and 3 more problems

1. An engineer is designing a wheelchair ramp that must have a maximum slope of 1:12 according to accessibility guidelines. The ramp needs to rise 2.5 feet to reach a building entrance. What angle, in degrees, should the ramp make with the horizontal ground? Round your answer to the nearest tenth of a degree.
2. Aroha is standing at the origin of a coordinate plane. She looks toward a point located at (15, 8). A line segment from the origin to this point forms an angle θ with the positive x-axis. Write an equation for θ using an inverse trigonometric function and solve for the measure of θ in degrees, rounded to one decimal place.
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (4,0), and (4,3). A line is drawn from the origin to the point (4,3), creating angle θ with the positive x-axis. What is the measure of angle θ in degrees? Use inverse trigonometric functions to find your answer.

…and 5 more problems