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Multi-Step Trigonometry Worksheets

Solve connected right-triangle problems by finding a shared length before calculating the requested measurement.

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Find shared measurements, then calculate the requested side or area.

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Transfer only the shared measurement

The connected triangles share an altitude. Solve one right triangle, then use that result in the second triangle or area calculation.

Learning objective

What this activity builds

Connect two right triangles through a shared measurement.

Worked example

Two right triangles share a height. One has base 12 and base angle 45 degrees; the other has base angle 30 degrees. Find the second base.

About 20.8.

The height is 12 tan(45 degrees) = 12. The second base is 12 / tan(30 degrees), about 20.8.

Teaching notes

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  • Mark the shared measurement.
  • Follow the selected intermediate-rounding policy.
  • Check that the final answer names the requested segment.

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Math SheetNameScoreTeacherDateMulti-Step TrigonometryDiagrams are not to scale. Introduce or use the altitude through D to form two right triangles, then complete the requested multi-step calculation. Round everycalculated step to the nearest tenth and use that rounded value in the next step.1.Drop altitude TD to LR, with foot D on LR. Find LR.LR = x12 yd42°54°LTRLR = ____ yd2.Use altitude TD, perpendicular to LR at D. Find LD.DLD = x8 mm35°44°LTRLD = ____ mmDiagrams are not to scale. Use degree mode.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateMulti-Step TrigonometryDiagrams are not to scale. Introduce or use the altitude through D to form two right triangles, then complete the requested multi-step calculation. Round everycalculated step to the nearest tenth and use that rounded value in the next step.3.Use altitude TD, perpendicular to LR at D. Find DR.DDR = x9 ft32°48°LTRDR = ____ ft4.Drop altitude TD to LR, with foot D on LR. Find TR.D10 cmTR = x44°50°LTRTR = ____ cmDiagrams are not to scale. Use degree mode.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateMulti-Step TrigonometryDiagrams are not to scale. Introduce or use the altitude through D to form two right triangles, then complete the requested multi-step calculation. Round everycalculated step to the nearest tenth and use that rounded value in the next step.5.Use altitude TD, perpendicular to LR at D. Find the area of triangle LTR.D11 in38°46°LTRArea = ____ in^26.Drop altitude TD to LR, with foot D on LR. Find the area of triangle LTR.14 mm40°52°LTRArea = ____ mm^2Diagrams are not to scale. Use degree mode.math-sheet.comPage 3 of 3

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