Question

2 multiple choice 1 point
find the area of the triangle. round your answer to the nearest tenth.
450 mm²
306.9 mm²
613.8 mm²
419.6 mm²

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle with two sides \(a\), \(c\) and included angle \(A\) is \(S=\frac{1}{2}ac\sin A\). Here \(a = 30\), \(c=30\), and \(A = 43^{\circ}\).

Step2: Substitute the values into the formula

Substitute \(a = 30\), \(c = 30\), and \(A=43^{\circ}\) into \(S=\frac{1}{2}ac\sin A\). We get \(S=\frac{1}{2}\times30\times30\times\sin43^{\circ}\).
Since \(\sin43^{\circ}\approx0.682\), then \(S=\frac{1}{2}\times30\times30\times0.682\).
First, calculate \(\frac{1}{2}\times30\times30 = 450\). Then \(S=450\times0.682\).

Step3: Calculate the result

\(450\times0.682 = 306.9\)

Answer:

\(306.9\space mm^{2}\)