Right Triangles and Trigonometry Flashcards

An airplane climbs at an angle of 15° from the horizontal. After traveling 4,000 feet along the flight path, how high has it climbed? (Use sin 15° ≈ 0.259)

Answer: 1,036 feet

Height = 4000 × sin(15°) = 4000 × 0.259 = 1,036 feet.

In right triangle ABC with right angle at C, the ratio BC : AC = 3 : 4. Which is the value of sin(A)?

Answer: 3/5

With BC = 3k and AC = 4k, the hypotenuse AB = 5k. sin(A) = BC/AB = 3k/5k = 3/5.

Two similar right triangles have perimeters 18 and 30. The smaller triangle has a hypotenuse of 8. What is the hypotenuse of the larger triangle?

Answer: 40/3

Scale factor = 30/18 = 5/3. Larger hypotenuse = 8 × (5/3) = 40/3.

In right triangle XYZ with right angle at Z, if sin(X) = a/b, what is the length of YZ in terms of a, b, and XY?

Answer: a·XY/b

sin(X) = YZ/XY = a/b, so YZ = a·XY/b.

A right triangle has legs in ratio 5:12. If the hypotenuse is 26, what is the shorter leg?

Answer: 10

The legs are 5k and 12k; hypotenuse = 13k = 26, so k = 2. Shorter leg = 5k = 10.

In right triangle ABC with right angle at C, AB = 34, BC = 16. Which expression gives tan(A)?

Answer: 16/√(34²−16²)

AC = √(34² − 16²) = √(1156 − 256) = √900 = 30. tan(A) = BC/AC = 16/30, which matches 16/√(34²−16²).

A ship sails 60 miles east and then 80 miles north. What is the straight-line distance from its starting point, and what angle (to the nearest degree) does this path make with the east-west axis?

Answer: 100 miles, 53°

Distance = √(60² + 80²) = √(3600+6400) = √10000 = 100 miles. tan(θ) = 80/60 = 4/3, so θ ≈ 53°.