Definitions 1
The longest side in a right triangle, across from the right angle.
A shape with three straight sides and three angles.
TRIANGLE
To find an answer using math (numbers).
CALCULATE
You use a ladder to reach a window. You know the angle the ladder makes with the ground. Which trig function could help you find how high the window is?
SINE
If you know the length of the shadow and the angle of the sun, which function helps you find the height of a tree?
TANGENT
The side across from the angle you are looking at.
OPPOSITE SIDE
The side next to the angle (but not the hypotenuse).
ADJACENT SIDE
A math function: adjacent side ÷ hypotenuse.
In a right triangle, the sine of an angle is the ratio of the opposite side to what?
If you’re standing on the ground and looking up at the top of a tree, what is the name of the angle you’re looking at?
THE ANGLE OF ELEVATION
A triangle with one 90° angle.
A RIGHT TRIANGLE
A math function: opposite side ÷ hypotenuse.
SINE
A guess or approximation.
ESTIMATE
If you know one angle and one side of a right triangle, which math function could you use to find another side?
SINE OR COSINE
An engineer uses cosine to calculate how far a crane's arm extends horizontally. Which two triangle parts is she comparing?
ADJACENT SIDE AND HYPOTENUSE
The angle from the ground up to something you’re looking at.
ANGLE OF ELEVATION
A unit used to measure angles.
DEGREE
The space between two lines that meet at a point.
A person looks up at a kite in the sky. They know their distance from the kite and the angle of elevation. What are they trying to calculate using sine?
In animation or video games, why are sine and cosine used in programming motion?
To create smooth circular or wave-like movement.
A comparison of two numbers, usually written as a fraction.
RATIO
A rule or formula that gives one result for each input.
FUNCTION
We can and should _______ math to real life. It isn't just theory.
Why do architects use sine and cosine when designing roofs?
To calculate slopes and structural support lengths.
A mountain slope rises at a 40° angle. A hiker climbs 500 meters along the slope. Using cosine, calculate the horizontal distance the hiker covered. (Round your answer)
approximately 383 meters (cos(40°) × 500 ≈ 383)