What is the area of triangle XYZ? Round to the nearest tenth of a square unit. Trigonometric area formula: Area 14.7 square units 14.9 square units 15.0 square units 15.3 square units

Complete Question:

The perimeter of triangle XYZ is 24 units. Triangle X Y Z is shown. The length of X Y is 3 and the length of Y Z is 11. Angle Y X Z is 102 degrees What is the area of triangle XYZ? Round to the nearest tenth of a square unit. Trigonometric area formula: Area 14.7 square units 14.9 square units 15.0 square units 15.3 square units

14.7 square units

Step-by-step Explanation:

Given the triangle shown in the figure attached below, having the following measures:

<YXZ = 102°

Length of XY = z = 3

Length of YZ = x = 11

Length of XZ = y = ?

Perimeter of ∆XYZ = x+y+z = 24 units

Length XZ = y, would be 11+y+3 = 24

14+y = 24

y = 24 - 14

Therefore, y = 10

==>Required:

Area of ∆XYZ to the nearest tenth of a square unit

==>Solution:

Using the Trigonometric area formula, area of ∆XYZ = ½(yz)sin X

Plug in values for x, y, and sin X:

Area of ∆ XYZ = ½×10×3×sin 102

= ½×30×0.9782

= 15 × 0.9782

= 14.673

Area of triangle XYZ approximated to the nearest tenth = 14.7 square units

x=half

step-by-step explanation: