Question

What is the approximate area of the triangle below?

a)72.8 sq. cm.
b)111.9 sq. cm.
c)142.0 sq. cm.
d)164.7 sq. cm.

Answer 1

Option a)72.8 sq. cm.

Explanation:

step 1

Find the measure of the third internal angle of the triangle

Remember that

the sum of the internal angles of a triangle must be equal to 180 degrees

so

95°+35°+A=180°

A=180°-95°-35°

A=50°

step 2

Applying the law of sines

Find the length side opposite to the angle of 35 degrees

14/sin(50°)=b/sin(35°)

b=[14/sin(50)]*sin(35)

b=10.48 cm

step 3

Applying the law of sines find the area of the triangle

A=(1/2)(14)(10.48)sin(95°)=73.10 cm²

therefore

The approximate area of the triangle below is 72.8 sq. cm

Answer 2

72.8 sq. cm

Explanation:

Given:

two angles and a side of a triangle that are 95°, 35° and 14 cm receptively

Area of triangle=?

Finding 3rd angle

=180-(95+35)

= 180-130

=50

Area of triangle can be calculated by using ASA i.e.

Area= a^2sinBsinC/2sinA

Putting values of a=14, B=95, C=35 and A=50, we get

Area= 14^2(sin95)(sin35)/2(sin50)

=98(0.74591)

=73.099

Closest option is a)72.8 sq. cm!