Answer
a) Angle A = 23°
b) Angle A = 49°
c) Angle A =
d) Angle A =
Step-by-step explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For these questions, using angle A as the non-right-angle angle,
a) Hypotenuse = AC = 18
Opposite = BC = 7
Adjacent = AB = ?
Angle = A
Trignometric ratios allow us to note that SOH means
Sin A = (Opp/Hyp)
Sin A = (7/18)
Sin A = 0.3889
A = Sin⁻¹ (0.3889) = 23°
b) Hypotenuse = AB = ?
Opposite = BC = 14
Adjacent = AC = 12
Angle = A
Trignometric ratios allow us to note that TOA means
Tan A = (Opp/Adj)
Tan A = (14/12)
Tan A = 1.1667
A = Tan⁻¹ (1.1667) = 49°
c) Hypotenuse = AC = 10
Opposite = BC = ?
Adjacent = AB = 6
Angle = A
Trignometric ratios allow us to note that CAH means
Cos A = (Adj/Hyp)
Cos A = (6/10)
Cos A = 0.60
A = Cos⁻¹ (0.6) = 53°
d) Hypotenuse = AB = ?
Opposite = BC = 200
Adjacent = AC = 288
Angle = A
Trignometric ratios allow us to note that CAH means
Cos A = (Adj/Hyp)
Cos A = (6/10)
Cos A = 0.60
A = Cos⁻¹ (0.6) = 53°