Question

Q.9 The measures of the angles of a triangle
are in the ratio 3:7:8. Find their measures
in degree and radian.
8​

Answer 1

Ratio of measure of angles of a ∆ is 3:7:8.

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✇ Let the angles of ∆ be 3x, 7x and 8x.

We know that,

★ The sum of all angles of a triangle is 180°.

➯ 3x + 7x + 8x = 180°

➯ 18x = 180°

➯ x = 180°/18

➯ x = 10

Therefore,

Measure of angles of triangle is,

• 3 × 10 = 30°

• 7 × 10 = 70°

• 8 × 10 = 80°

∴ Measure of angles in degree are 30°, 70° and 80°.

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Now, We have to convert degree into radian -

We know that,

⠀⠀⠀ ★ Radian = 1 × π/180°

Therefore,

• 30° × π/180° = π/6° Radian

• 70° × π/180° = 7π/18° Radian

• 80° × π/180° = 4π/9° Radian

∴ Measure of angles in radian are π/6° , 7π/18° and 4π/9°.