Question

What is the approximate area of the triangle below? 95 degrees 35 degrees 14cm.

Answer 1

By utilizing the law of the sines and Heron's formula, we find that the approximate area of the triangle is approximately 73.1 square centimeters. (Correct choice: A)

How to calculate the area of a triangle by Heron's formula

Prior to using Heron's formula, we must find the lengths of the missing sides by law of the sines:

A = 180° - 95° - 35°

A = 50°

$b = 14\,cm \times \frac{\sin 35^{\circ}}{\sin 50^{\circ}}$

b ≈ 10.483 cm

$c = 14\,cm \times \frac{\sin 95^{\circ}}{\sin 50^{\circ}}$

c ≈ 18.206 cm

Now, we proceed to calculate the area of the triangle:

s = 0.5 · (14 cm + 10.483 cm + 18.206 cm)

s = 21.345 cm

$A = \sqrt{(21.345\, cm) \cdot (21.345\, cm - 14\,cm)\cdot (21.345\, cm - 10.483\,cm)\cdot (21.345\,cm - 18.206\,cm)}$

A ≈ 73.113 cm²

By utilizing the law of the sines and Heron's formula, we find that the approximate area of the triangle is approximately 73.1 square centimeters. (Correct choice: A)

To learn more on triangles: brainly.com/question/2773823

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