Question

What is the approximate area of the triangle below?

73.1 sq. cm.
111.7 sq. cm.
141.4 sq. cm.
164.7 sq. cm.

Answer 1

Answer: A 73.1

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Answer 2

73.1 cm²

Step-by-step explanation:

We need to know at least two of the side lengths of the triangle that makes one of the angles given an included angle.

Find the measure of the third angle, the angle that is opposite 14 cm:

Thus,

180 - (95 + 35) = 50°

Using Sine rule, let's find the side length that is opposite to 35°:

Let the side length opposite to 35° be represented as "x".

Thus:

x/sin(35) = 14/sin(50)

Multiply both sides by sin(35)

x = 14/sin(50) × sin(35)

x = (14×sin(35))/sin(50)

x = 10.5 cm (nearest tenth)

✔️Use ½*a*b*sin(C) to find the area

where,

a = 14 cm

b = 10.5 cm

C = 95°

Plug in the values

Area = ½*14*10.5*sin(95)

Area ≈ 73.1 cm²