Question 1: Calculate sin 30° and cos 45°.

Answer: sin 30° = 1/2, cos 45° = √2/2

Question 2: Find tan 60° using exact values.

Answer: √3

Question 3: Construct a right triangle with a 45° angle and hypotenuse of length 10 units. Calculate the lengths of the other two sides.

Answer: legs = 10/√2 ≈ 7.07 units each

Question 4: Determine sin 60° and cos 30° using exact values.

Answer: sin 60° = √3/2, cos 30° = √3/2

Question 1: A ladder leans against a wall, forming a 60° angle with the ground. If the ladder is 12 meters long, how high does it reach on the wall?

Answer: 10.39 meters

Question 2: A ramp is inclined at 30°. If the ramp length is 15 meters, what is the height of the ramp from the ground?

Answer: Height ≈ 7.5 meters

Question 3: Construct a triangle with a 45° angle, hypotenuse of 8 units, and find the length of the opposite side.

Answer: opposite side = 8/√2 ≈ 5.66 units

Question 1: A kite is flying at a position where the string makes a 45° angle with the ground. If the string length is 20 meters, how high is the kite?

Answer: Height ≈ 14.14 meters

Question 2: A flagpole casts a shadow that is 10 meters long when the sun is at a 30° angle. How tall is the flagpole?

Answer: Flagpole height ≈ 5.77 meters

Question 1: Construct a right triangle where one angle is 60° and the hypotenuse is 15 units. Calculate the lengths of the other sides.

Answer: Opposite side ≈ 13.0 units, adjacent side ≈ 7.5 units

Question 2: A ramp makes a 30° angle with the ground. If the height of the ramp is 9 meters, what is the length of the ramp?

Answer: Ramp length ≈ 17.5 meters

Question 1: Calculate sin 45° and tan 30°.

Answer: sin 45° = √2/2, tan 30° = 1/√3

Question 2: Construct a triangle with hypotenuse 10 units and one angle of 60°. Find the length of the side opposite to 60°.

Answer: Side ≈ 5 units

Question 1: A student claims that cos 45° = 1/2. Identify and explain the mistake.

Answer: Misconception: cos 45° = √2/2, not 1/2.