Question

What the answer now now

Answer 1

Answer:

The area of the triangle is $346.0\ mm^2$

Step-by-step explanation:

Given

Triangle VWU

Required

Determine the Area of the Triangle

First, we'll solve for the third angle

Angles in a triangle when added equals 180;  So

$36 + 24 +$

$60 +$

Next is to determine the length of VW using Sine Law which goes thus

$\frac{VW}{Sin24} = \frac{34}{Sin36}$ (Because 24 degrees is the angle opposite side VW)

Multiply both sides by Sin24

$SIn24 * \frac{VW}{Sin24} = \frac{34}{Sin36} * Sin24$

$VW = \frac{34}{Sin36} * Sin24$

$VW = \frac{34}{0.5878} * 0.4067$

$VW = 23.5 mm$ (Approximated)

At this stage, we have two known sides and two known angles;

The Area can be calculated as the 1/2 * the products of two sides * Sin of the angle between the two sides

Considering VW and VU

VW = 23.5 (Calculated);

VU = 34 (Given)

The angle between these two sides is 120 (Calculated);

Hence;

$Area = \frac{1}{2} * 23.5 * 34 * Sin120$

$Area = \frac{1}{2} * 23.5 * 34 * 0.8660$

$Area = \frac{1}{2} * 691.934$

$Area = 346.0 mm^2$

Hence, the area of the triangle is $346.0\ mm^2$