Right Triangles and Trigonometry Flashcards

In right triangle ABC with right angle at C, sin(A) = 2√5/5. What is tan(A)?

Answer: 2

sin(A) = 2√5/5, so opposite = 2√5 and hypotenuse = 5. Adjacent = √(25 − 20) = √5. tan(A) = 2√5/√5 = 2.

A 45-45-90 triangle has area 72. What is the perimeter?

Answer: 24 + 12√2

Area = (1/2)s² = 72 so s = 12. Hypotenuse = 12√2. Perimeter = 12 + 12 + 12√2 = 24 + 12√2.

In right triangle PQR with right angle at R, if cos(P) = x, what is tan(Q)?

Answer: x/√(1−x²)

Angles P and Q are complementary, so sin(Q) = cos(P) = x and cos(Q) = sin(P) = √(1−x²). Thus tan(Q) = sin(Q)/cos(Q) = x/√(1−x²).

A vertical pole casts a shadow 20 feet long. The sun's rays make a 60° angle with the ground. How tall is the pole?

Answer: 20√3

tan(60°) = height/20, so height = 20·tan(60°) = 20√3.

In right triangle ABC, the right angle is at C. If BC = 7 and angle A = 45°, what is AB?

Answer: 7√2

sin(45°) = BC/AB = 7/AB, so AB = 7/sin(45°) = 7/(√2/2) = 7·2/√2 = 14/√2 = 7√2.

Right triangles DEF and GHI are similar, with DE:GH = 3:7. If the area of triangle DEF is 9 square units, what is the area of triangle GHI?

Answer: 49

Areas of similar figures scale as the square of the linear scale factor. (7/3)² × 9 = (49/9) × 9 = 49.

In right triangle ABC with right angle at C, AB = 10 and cos(A) = 3/5. What is the area of the triangle?

Answer: 24

cos(A) = AC/AB = AC/10 = 3/5, so AC = 6. BC = √(100−36) = 8. Area = (1/2)(6)(8) = 24.