Question

Triangle a b c is shown. Angle b c a is a right angle. The length of hypotenuse b a is 9. 8 inches, the length of c b is 6. 3 inches, and the length of c a is 7. 5 inches. Which expressions can be used to find m∠abc? select two options. Cos−1(startfraction 9. 8 over 6. 3 endfraction) cos−1startfraction 6. 3 over 9. 8 endfraction) cos−1(startfraction 7. 5 over 9. 8 endfraction) sin−1(startfraction 9. 8 over 7. 5 endfraction) sin−1(startfraction 7. 5 over 9. 8 endfraction).

Answer 1

The expressions used to find m∠abc is cos⁻¹(6.3/9.8) and sin⁻¹(7.5 / 9.8).

Trigonometric ratio

Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.

Given triangle ABC with side ba as the hypotenuse. Let θ represent m∠abc, hence using trigonometric ratios:

sinθ = 7.5 / 9.8

θ = m∠abc = sin⁻¹(7.5 / 9.8)

Also:

cosθ = 6.3 / 9.8

θ = m∠abc = cos⁻¹(6.3/9.8)

The expressions used to find m∠abc is cos⁻¹(6.3/9.8) and sin⁻¹(7.5 / 9.8).

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