Question

Given the right triangle shown, solve for X, Y and Z. The triangle may not be drawn to scale

Answer 1

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°