The size of the angle marked x is 33.6°, using trigonometric ratios.
Trigonometric ratios are used in right triangles for the ratios of any two sides with respect to any acute angle of that triangle.
In the question, we are asked to find the size of the angle marked x.
In the given triangle, PQR, we can see that ∠Q = 90°.
By trigonometric ratios, we know that:
cos ∠R = QR/PR,
or, ∠R = cos ⁻¹ (QR/PR),
or, ∠R = cos ⁻¹ (15/18),
or, ∠R = cos ⁻¹ (5/6),
or, ∠R = cos ⁻¹ (cos 33.55730976°),
or, ∠R = 33.55730976°,
or, ∠R ≈ 33.6°.
Thus, the size of the angle marked x is 33.6°, using trigonometric ratios.
Learn more about trigonometric ratios at
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