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
Answer:
14.7 square units
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