Find the area

Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.

A = 50°, b = 30 ft, c = 14 ft


Result

A =  160.87 ft2

Solution:

a2=b2+c2−2bccos⁡A a=302+142−2⋅30⋅14⋅cos⁡50∘=23.581 ft s=12(a+b+c)=33.7905 ft S=s(s−a)(s−b)(s−c)=160.87 ft2a^2 = b^2+c^2 - 2bc \cos A \ \\ a = \sqrt{ 30^2 + 14^2 -2\cdot 30\cdot 14 \cdot \cos 50^\circ } = 23.581 \ ft \ \\ s = \dfrac12(a+b+c) = 33.7905 \ ft \ \\ S = \sqrt{s(s-a)(s-b)(s-c)} = 160.87 \ ft^2

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Tips to related online calculators
See also our right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

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