G.5.TM.6
Apply right-triangle relationships using Pythagorean Theorem, special right triangles, and trigonometry in real-world scenarios (e.g., roof construction, building the frame of a car, calculating machined parts)
Example Problems
A ‑foot ladder leans against a vertical wall. The base of the ladder is feet from the wall.
How high up the wall does the ladder reach?
How high up the wall does the ladder reach?
A square tile measures 15 centimeters on each side.
What is the diagonal distance across the tile?
Write your answer as a decimal rounded to the nearest hundredth.
What is the diagonal distance across the tile?
Write your answer as a decimal rounded to the nearest hundredth.
Aria runs 5 miles east and then a certain number of miles north.
She ends 13 miles away from her starting position.
How many miles north did Aria run?
She ends 13 miles away from her starting position.
How many miles north did Aria run?
Khan Academy ResourcesSide ratios in right triangles as a function of the anglesIntro to inverse trig functionsSolving for a side in right triangles with trigonometryAngles of elevation and depressionTrigonometric ratios in right trianglesRight triangle trigonometry reviewSpecial right triangles reviewHypotenuse, opposite, and adjacentSolve for a side in right trianglesSpecial right trianglesTrigonometric ratios in right trianglesPythagorean theorem in 3DPythagorean theorem challengeUse ratios in right trianglesSolve for an angle in right trianglesRight triangle trigonometry word problemsSolving for a side in right triangles with trigonometryTrigonometric ratios in right trianglesSpecial right triangles proof (part 2)Special right triangles proof (part 1)30-60-90 triangle example problemArea of a regular hexagonPythagorean theorem in 3DUsing similarity to estimate ratio between side lengthsMulti-step word problem with Pythagorean theoremRight triangle word problemPythagorean theorem with isosceles triangleTriangle similarity & the trigonometric ratiosUsing right triangle ratios to approximate angle measure

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