The area of a triangle is 70 in². Find the length of the side included between the angles Round to three significant digits. A)11.9 in B)12.1 in C)12.5 in D)12.3 in E)12.7 in

Question

Quizplus · Accepted Answer

We can use the formula for the area of a triangle:
Area = (1/2) * base * height

Let the side included between the angles be x, and let the height of the triangle be h. Then we have:

Area = (1/2) * x * h = 70

Solving for h, we get:

h = (2 * Area) / x = 140 / x

Now, we can use the law of sines to relate the height to the sides of the triangle:

sin(60) / x = sin(75) / h

Substituting for h and simplifying, we get:

sin(60) * x = sin(75) * (140 / x)

Multiplying both sides by x, we get:

sin(60) * x^2 = (140 / x) * sin(75) * x

Simplifying and solving for x, we get:

x = (140 * sin(75)) / (sin(60) * x)

x^2 = (140 * sin(75)) / sin(60)

x = sqrt((140 * sin(75)) / sin(60)) ≈ 12.726

Rounding to three significant digits, we get:

x ≈ 12.7

Therefore, the answer is choice E, 12.7 in.

The Area of a Triangle Is 70 In2

The Area of a Triangle Is 70 In²