Back to the lesson

Right Triangles and Trigonometry flashcards

0/15

15 cards remaining

All 15 cards in this deckShow
How do you find the hypotenuse of a right triangle from its legs?Pythagorean Theorem
c = √(a² + b²): square the legs, add them, then take the square root.
How do you find a missing leg of a right triangle?Pythagorean Theorem
a = √(c² − b²): subtract the square of the known leg from the square of the hypotenuse.
How can you tell whether three side lengths form a right triangle?Pythagorean Theorem
Check whether a² + b² = c², where c is the longest side. If so, the triangle is right.
What are the side ratios in a 45°–45°–90° triangle?Special Right Triangles
1 : 1 : √2. The legs are equal and the hypotenuse is a leg times √2.
What are the side ratios in a 30°–60°–90° triangle?Special Right Triangles
Short leg : long leg : hypotenuse = 1 : √3 : 2.
In a special right triangle, how do you tell which side is which?Special Right Triangles
First see which angle a side faces; that tells you whether it is the short leg, long leg, or hypotenuse.
What is the sine of an acute angle in a right triangle?Sine, Cosine, and Tangent
sin θ = opposite ÷ hypotenuse.
What is the cosine of an acute angle in a right triangle?Sine, Cosine, and Tangent
cos θ = adjacent ÷ hypotenuse.
What is the tangent of an acute angle in a right triangle?Sine, Cosine, and Tangent
tan θ = opposite ÷ adjacent.
How do you find an unknown side of a right triangle using trig?Solving Right Triangles
Label the sides around the known angle, choose the ratio with your known side and missing side, then solve.
How do you find an unknown acute angle of a right triangle?Solving Right Triangles
Form a side ratio, then use the inverse trig function, such as θ = tan⁻¹(opposite ÷ adjacent).
How are the two acute angles of a right triangle related?Solving Right Triangles
They are complementary; they add to 90°.
What is an angle of elevation?Applications of Trigonometry
The angle measured upward from the horizontal to an object above the viewer.
What is an angle of depression?Applications of Trigonometry
The angle measured downward from the horizontal to an object below the viewer.
How do you set up a height-and-distance word problem with trig?Applications of Trigonometry
Sketch the height and horizontal distance as the legs of a right triangle before choosing sine, cosine, or tangent.