Right Triangles and Trigonometry Flashcards

In right triangle ABC with right angle at C, if sin(A) = k, what is cos(B)?

Answer: k

Angles A and B are complementary (sum to 90°), so cos(B) = cos(90° − A) = sin(A) = k.

A right triangle has a leg of 15 and a hypotenuse of 17. What is the area of the triangle?

Answer: 60

The other leg = √(289 − 225) = √64 = 8. Area = (1/2)(15)(8) = 60.

From a window 40 feet above the ground, the angle of depression to a car parked on the street is 45°. How far is the car from the building (horizontal distance)?

Answer: 40 feet

The angle of depression equals the angle of elevation from the car. tan(45°) = 40/d, so d = 40.

In a right triangle, the ratio of the two legs is 1:√3. Which of the following describes the acute angles?

Answer: 30° and 60°

A ratio of legs 1:√3 matches the 30-60-90 triangle, where the opposite sides are in ratio 1:√3:2.

In right triangle RST with right angle at S, RS = a and ST = b. Which expression gives sin(T)?

Answer: a/√(a²+b²)

The hypotenuse RT = √(a²+b²). sin(T) = opposite/hypotenuse = RS/RT = a/√(a²+b²).

A right triangle has one leg of length 8 and the angle opposite that leg measures 60°. What is the hypotenuse?

Answer: 16√3/3

sin(60°) = 8/hypotenuse, so hypotenuse = 8/sin(60°) = 8/(√3/2) = 16/√3 = 16√3/3.

In right triangle ABC with right angle at C, tan(A) = 5/12 and BC = 10. What is AB?

Answer: 26

tan(A) = BC/AC = 10/AC = 5/12, so AC = 24. Then AB = √(10² + 24²) = √(100 + 576) = √676 = 26.