1 Answer

Shohn · Answer 1 · 2024-04-15T09:26:39+0000

The area of the triangle is: b) 122.49 square units

Using the given values, we can use the Law of Cosines to find the third side of the triangle, which is side c.

$[ c^2 = a^2 + b^2 - 2ab\cos(c) ]\\[ c^2 = 20^2 + 17^2 - 2(20)(17)\cos(68^\circ 52') ]\\[ c^2 \approx 576.98 ]\\[ c \approx 24.01 ]$

Now that we have all three sides of the triangle, we can use Heron's formula to find the area of the triangle.

$[ s = (a+b+c)/(2) = (20+17+24.01)/(2) \approx 30.51 ]$

$[ A = √(s(s-a)(s-b)(s-c)) \approx 122.49 ]$

Rounding to the nearest hundredth, the area of the triangle is approximately 122.49 square units. Therefore, the answer is:

b) 122.49 square units

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