Question 1: Calculate the length of side BC in a right triangle ABC where angle A is 30°, AB (adjacent to angle A) is 10 units, and BC is opposite to angle A. (Use TOA ratio)

Answer: 5.77

Question 2: In triangle XYZ, angle Y is 45°, XY (adjacent to Y) is 8 units. Find the length of YZ (opposite to Y).

Answer: 8

Question 3: A ladder leans against a wall forming a 60° angle with the ground. The ladder's base is 4 meters from the wall. What is the height the ladder reaches on the wall?

Answer: 6.93

Question 4: Identify the common mistake: A student calculates the opposite side as 7 units given tan(45°) = Opposite / Adjacent, with Adjacent = 7 units, and gets 7 as answer. What is the mistake?

Answer: They used tan(45°)=Opposite/Adjacent but since tan(45°)=1, Opposite=Adjacent=7 units. No mistake; trick question.

Question 1: Triangle PQR has angle P = 20°, QR (opposite P) is 10 units, and PR (adjacent to P) is unknown. Find PR.

Answer: 36.4

Question 2: In a right triangle, the opposite side is 15 units, and the angle is 60°. Find the length of the adjacent side using TOA.

Answer: 8.66

Question 3: A tree casts a shadow 12 meters long when the angle of elevation from the tip of the shadow to the top of the tree is 30°. How tall is the tree?

Answer: 6.93

Question 4: Explain why using tan(45°)=Opposite/Adjacent helps find the side length in a right triangle when the angle is 45°.

Answer: Because tan(45°)=1, Opposite=Adjacent, making calculations straightforward.

Question 1: A person stands 20 meters from a building and measures the angle of elevation to the top as 35°. Find the height of the building. (Ignore the height of the person's eye level.)

Answer: 15.09

Question 2: A flagpole casts a 9-meter shadow when the sun's angle is 45°. How tall is the flagpole?

Answer: 9

Question 3: A ladder leaning against a wall makes a 75° angle with the ground. The top of the ladder reaches 8 meters high. How long is the ladder?

Answer: 21.89

Question 1: A surveyor measures the angle of elevation from a point on the ground to the top of a hill as 25°. If the distance from the point to the base of the hill is 150 meters, estimate the height of the hill.

Answer: 68.1

Question 2: A person looks up at an angle of 60° at a lighthouse 50 meters high. How far away is the person from the lighthouse?

Answer: 28.87

Question 1: In triangle DEF, angle D is 40°, DE is 12 units, and DF is unknown. Find the length of DF.

Answer: 15.84

Question 2: A drone flies at an altitude of 120 meters. From a certain point on the ground, the angle of elevation to the drone is 45°. How far is the drone horizontally from that point?

Answer: 120

Question 1: A student calculates the opposite side as 9 units given tan(30°) = Opposite / Adjacent, with Adjacent = 10 units. Is this correct? Why or why not?

Answer: No, because tan(30°)=Opposite/Adjacent=1/√3≈0.577, so Opposite=Adjacent×tan(30°)=10×0.577≈5.77 units.

Question 2: If a student uses sine instead of tangent to find a side in a right triangle where TOA applies, what mistake are they making?

Answer: They are mixing ratios; sine relates opposite/hypotenuse, not opposite/adjacent.