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Finding Ratios and Angles in Right-Angled Triangles

Learn how to calculate ratios, sides, and angles in right-angled triangles using the tangent ratio and a calculator.

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Finding Ratios and Angles in Right-Angled Triangles

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  1. What is the ratio for a 600 right-angled triangle? opposite opposite adjacent adjacent = 1.7 = (to 1 decimal place) opp 4.5 4.5cm similar triangles have all corresponding angles equal All the “600“right-angled triangles will be similar – so the ratio will be 1.7 for all your triangles. Label the opposite and adjacent sides. adj 600 2.7cm 2.7

  2. 1.7 for these triangles. We know that opposite opp 600 adjacent 12cm 3cm opp adj x = opp x 600 adj 600 adj x = 1.7 5cm x x x = 1.7 = 5.1cm 3 1.7 = = 1.7 12 x x 12 x x 5 3 1.7 = x x = 1.7 = 8.5cm x 5 7.1cm = x

  3. 0.8 Answers for 400 triangles: opposite adjacent What’s the size of angle y? = Qus 1: x = 0.8 x 8 = 6.4cm 17cm Qus 2: x = 9 ÷ 0.8 = 11.25cm y = 600 y 10cm

  4. The ratio we have been working out is called the Tangent Ratio. We can look up tangent ratios for different angles using the following table. As long as we know the tangent ratio for a particular right-angled triangle we can calculate sides and angles.

  5. Use the table to find: tan 620 = 1.8807 We can look up tangent ratios for different angles using the following table. tan 750 = 3.7321 inverse of tan – use to find an angle tan-11.3764 = 540

  6. Use the tangent ratio to find x in each of these triangles. 6.3cm 270 7cm x x 540 x 10.6cm 8.2cm Click on a triangle to see the solution for that triangle. 4.8cm skip solutions

  7. Use the tangent ratio to find x in each of these triangles. opposite Tan 540 = adjacent opp x x Tan 540 = 8.2 540 x 8.2cm x x Tan 540 = 8.2 adj 8.2 x 1.3764 = x 11.3 = x back

  8. Use the tangent ratio to find x in each of these triangles. 6.3cm opposite Tan x0 = opp adjacent 6.3 7cm Tan x0 = 7 adj x 0.9 Tan x0 = x = 420 back

  9. Use the tangent ratio to find x in each of these triangles. opposite Tan 270 = adjacent 270 4.8 Tan 270 = x x 10.6cm adj 4.8 = Tan 270 = x x = 9.4cm 4.8cm opp back

  10. Using a Calculator We looked these up earlier using a tangent table, but it’s more convenient to use a calculator. tan 620 = 1.8807 tan 750 = 3.7321 tan 62 = Type: tan-1 1.3764 = 540 tan 75 = For tan-1 use your shift or 2nd button tan-1 1.3764 = tan shift

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