Question

Using trigonometry Solve the triangle please help me

Answer 1

The angle m ∠ W = 33°

The length of XZ = 9.8 units

The length of WX = 15.1 units

Explanation:

Given

The right-angled triangle ΔWXZ

• m ∠ X = 90°

• m ∠ Z = 57°

• Hypotenuse WZ = 18

We know that the sum of the measure of angles in any triangle is 180°.

Therefore,

m ∠ W + m ∠ X + m ∠ Z = 180°

substiute m ∠ X = 90° and m ∠ Z = 57° in the formula

m ∠ W + 90° + 57° = 180°

m ∠ W + 147 = 180°

m ∠ W = 180° - 147

m ∠ W = 33°

Therefore, the angle m ∠ W = 33°

NOW,

Determining the lengths of WX and XZ

Length XZ

Using the trigonometric ratio

The adjacent to 57° is XZ.

so

cos 57° = adjacent / hypotenuse

substituting adjacent = XZ, and hypotenuse = 18

cos 57° = XZ / 18

XZ = 18 × cos 57°

XZ = 9.80 units

Therefore, the length of XZ = 9.8 units

Length WX

As

m ∠ W = 33°

The adjacent to m ∠ W = 33° is WX.

so

cos 33° = adjacent / hypotenuse

substituting adjacent = WX, and hypotenuse = 18

cos 33° = WX/ 18

WX = 18 × cos 33°

WX = 15.1 units

Therefore, the length of WX = 15.1 units

Summary:

The angle m ∠ W = 33°

The length of XZ = 9.8 units

The length of WX = 15.1 units