find (acute) angle A, given:
a. sin A = 0.4919
b. tan A = 2.7775
c. cos A = 0.5757
To find the acute angle A using trigonometric functions, we can use the inverse trigonometric functions. Different trigonometric functions will require different inverse functions to find the angle.
a. Given sin A = 0.4919, we can use the arcsine (or sin^(-1)) function to find angle A.
A = arcsin(0.4919)
Use a scientific calculator or lookup table to find the inverse sine of 0.4919.
A ≈ 29.06 degrees
b. Given tan A = 2.7775, we can use the arctan (or tan^(-1)) function to find angle A.
A = arctan(2.7775)
Use a scientific calculator or lookup table to find the inverse tangent of 2.7775.
A ≈ 70.32 degrees
c. Given cos A = 0.5757, we can use the arccosine (or cos^(-1)) function to find angle A.
A = arccos(0.5757)
Use a scientific calculator or lookup table to find the inverse cosine of 0.5757.
A ≈ 54.89 degrees
Please note that the angles provided are approximate and rounded to two decimal places.