Question

How will we solve this?

These are my thoughts:
1. We are only given two sides, so if we wanted to use cosine or sine that wouldn't work.
2. This is not a right angled diagram so the primary trigonometric ratio wouldn't apply here.
3. Since two sides should be congruent I get that the base of the next triangle would be 3.8 as well.

Answer 1

a)

You are given 3 sides.

The single stroke on each side of the triangle means the two sides are equal.

So the three sides are: 3.8m, 3.8m and 4.8m

To get the angle we use cosine rule:

Cos A = (b² + c² - a²)/(2bc)

Let us solve for the angle facing the 3.8

Cos A = (4.8² + 3.8² - 3.8²) / (2*3.8*4.8)

Cos A = (4.8²) / (2*3.8*4.8) = 4.8/(2*3.8) ≈ 0.6316

A = Cos⁻¹(0.6316)

A ≈ 50.8°

Since the triangle is Isosceles triangle, since the side 3.8 are two, so the angles facing it would be same.

50.8° and 50.8°

To solve for the third angle.

Sum of angles in a triangle = 180

50.8 + 50.8 + x = 180

x =180 - 50.8 -50.8

x = 78.4°

So the interior angles in the triangle ≈ 50.8°, 50.8°, 78.4°

b)

Area of triangle: Using Hero's formula, that is when the three sides of the triangle are given.

3.8, 3.8, and 4.8, a = 3.8, b = 3.8, c = 4.8

Hero's formula = √(s(s - a)(s - b)(s - c))

s = (a + b + c)/2

s = (3.8 + 3.8 +4.8)/2 = 12.4/2 = 6.2

Area = √(s(s-a)(s-b)(s-c))

Area = √(6.2* (6.2 - 3.8)* (6.2 - 3.8)* (6.2 - 4.8))

Area = √(6.2* 2.4* 2.4* 1.4) = √49.9968

Area ≈ 7.07 square meter

For the two triangles ≈2*7.07 ≈ 14.14 square meter.

Hope this helps.