In a right-angled triangle (XYZ ) with ( Z = 90^ )

MATHEMATICS · Subjective · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

In a right-angled triangle XYZXYZ with ∠Z=90∘\angle Z = 90^\circ, the perimeter of the triangle is 30 cm30\,\text{cm} and the acute angle ∠X=60∘\angle X = 60^\circ. (i) Express the lengths of YZYZ (opposite ∠X\angle X) and XZXZ (adjacent to ∠X\angle X) in terms of a single variable. (ii) Form an equation in that variable using the perimeter and solve for the exact lengths of all three sides. (iii) Calculate the area of △XYZ\triangle XYZ in square centimetres.

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