Question

find the length of side c.

(there is a triangle abc with angle c = 100°, side a = 30, side b = 25, and side c is unknown, marked as ?)

law of cosines: $c^2 = a^2 + b^2 - 2ab \cdot \cos(c)$
round your answer to the nearest hundredth.

Explanation:

Step1: Identify given values

We have \( a = 30 \), \( b = 25 \), and \( C = 100^\circ \). We will use the Law of Cosines formula \( c^2=a^2 + b^2-2ab\cdot\cos(C) \).

Step2: Substitute values into formula

Substitute \( a = 30 \), \( b = 25 \), and \( \cos(100^\circ) \) (we know that \( \cos(100^\circ)\approx - 0.1736 \)) into the formula:

$$
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Step3: Solve for \( c \)

Take the square root of \( c^2 \) to find \( c \):
\( c=\sqrt{1785.4}\approx42.25 \) (rounded to the nearest hundredth)

Answer:

\( 42.25 \)