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Trigonometry, how would I find the area of this triangle?

Trigonometry, how would I find the area of this triangle?-example-1

2 Answers

6 votes

Use sine rule for Area


\\ \rm\rightarrowtail Area=(1)/(2)absinC


\\ \rm\rightarrowtail Area=(1)/(2)(3.9)(5.6)sin56°45'


\\ \rm\rightarrowtail Area=10.92(0.836)


\\ \rm\rightarrowtail Area=10.22cm^2

User Oklahomer
by
3.6k points
7 votes

Answer:

Explanation:

Area of triangle = 1/2 * base * height

Use the side of length 5.6cm as base, the height will be a perpendicular line from the base to the tip of the triangle.

From the right-angle triangle formed by the height and the side of length 3.9cm,

sin(56°45') = height / 3.9

height = 3.9*sin(56°45')

Substituting back into the area equation:

Area = 1/2*5.6*3.9*sin(56°45')

= 9.0cm^2

= 9cm^2

User Engel
by
3.6k points