Answer:
- X ≈ 8.58 ft
- Y ≈ 9.46 ft
- Z = 65°
Step-by-step explanation:
The mnemonic SOH CAH TOA is intended to help you remember the relationships between sides of a right triangle and trig functions of the acute angles. It tells you ...
- Sin = Opposite/Hypotenuse
- Cos = Adjacent/Hypotenuse
- Tan = Opposite/Adjacent
Sides
The given triangle shows values of an acute angle and its opposite side. You are to find the other two sides in the triangle, as well as the other acute angle.
X is the side adjacent to the given angle, so the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(25°) = (4 ft)/X
Solving for X gives ...
X = (4 ft)/tan(25°) . . . . . . . . multiply by X/tan(25°)
X ≈ 8.58 ft
Y is the hypotenuse, so the relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(25°) = (4 ft)/Y
Y = (4 ft)/sin(25°) . . . . . . multiply by Y/sin(25°)
Y ≈ 9.46 ft
Angle
The sum of angles in a triangle is 180°, so if one of them is 90°, the sum of the other two is 90°.
Z = 90° -25°
Z = 65°
