Instructions
Complete the following exercises on trigonometry. Show all your work for full credit.
Part 1: Trigonometric Ratios
1. In a right triangle, if one of the angles is 30 degrees and the hypotenuse is 10 cm, find the lengths of the opposite and adjacent sides. Use trigonometric ratios to support your answer.
2. If sin(θ) = 0.5, what is the value of θ? Express your answer in degrees.
Part 2: Solving Right Triangles
3. A right triangle has one angle measuring 45 degrees and a hypotenuse of 14 cm. Calculate the lengths of the other two sides.
4. Find the length of the hypotenuse of a right triangle if one leg measures 5 cm and the other leg measures 12 cm.
Part 3: Application Problems
5. A ladder is leaning against a wall making an angle of 60 degrees with the ground. If the foot of the ladder is 4 meters away from the wall, how high up the wall does the ladder reach?
6. An airplane is flying at an altitude of 1,000 meters. When it is 2,000 meters horizontally from the airport, at what angle is it approaching the airport? (Use the tangent function)