Grade 10 Academic (MPM2D) · Trigonometry

Similar triangles

Use similar-triangle ratios to find a missing side, both in abstract triangle notation and in an indirect-measurement word problem. Unlimited questions, five difficulty levels, and a full worked solution every time — free.

Practice this skill Curriculum: MPM2D-TR1.1

Try one

On a sunny afternoon, a rake leaning straight up and a grain elevator cast shadows at the same time. Because the sun hits them at the same angle, height and shadow length are proportional for both. The rake is 5 m tall and casts a 8 m shadow. The grain elevator casts a 32 m shadow. How tall is the grain elevator?

Answer: 20

See one solved, step by step

Triangle ABC is similar to triangle DEF. AB = 3, DE = 9, and BC = 7. Find the length of EF.

📘 Worked solution

1AB corresponds to DE, and BC corresponds to EF (matching vertex order).In similar triangles, corresponding sides are in the same ratio, and vertex order tells you which sides match up.

2Scale factor = DE/AB = 93 = 3Divide a known pair of corresponding sides to find the scale factor from triangle ABC to triangle DEF.

3EF = BC · 3 = 7 · 3 = 21Multiply BC by the same scale factor to find EF.

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