Question

Find the area of triangle ABC.A. 13.1 units²B. 21.61 units²C. 30.3 units²D. 14.65 units²

Answer 1

Given in the following figure:

AB = 4.25

AC = 6.93

∠A = 84.08°

∠B = 62.86°

With the following given, for us to be able to get the area of the triangle, we will be using the following formula:

$\text{ Area = }\frac{\text{ ab x sin(}\angle\text{C)}}{\text{ 2}}$

Where,

a and b are two adjacent sides of the triangle and ∠C is the angle between the two sides.

From the given, AB and AC are adjacent sides and the angle between them is ∠A.

Now, from the formula that we will be using, let:

a = AB = 4.25

b = AC = 6.93

∠C = ∠A = 84.08°

We get,

$\text{ Area = }\frac{\text{ ab x sin(}\angle\text{C)}}{\text{ 2}}$$\text{ = }\frac{(4.25)(6.93)\text{ x sin (}84.08\degree)}{2}$$\text{ = }\frac{(29.4525)\text{ x sin (}84.08\degree)}{2}$$\text{ = (}14.72625)\text{ x sin (}84.08\degree)$$\text{ Area = 14.647713 }\approx\text{ 14.65 sq. units}$

Therefore, the answer is letter D.