Question

In ABC, BC=4 Centimeters, mB = mC, and mA = 20 degrees What is AC to two decimal places?

Answer 1

To find AC in ΔABC with BC = 4 centimeters, mB = mC, and mA = 20 degrees, we can use the Law of Sines to solve for AC.

Step-by-step explanation:

In ΔABC, BC = 4 centimeters, mB = mC, and mA = 20 degrees. To find AC, we can use the Law of Sines.

Using the Law of Sines, we have the equation:

AC / sin(A) = BC / sin(C)

Plugging in the known values, we get:

AC / sin(20°) = 4 / sin(C)

Now, we can solve for AC:

AC = (4 / sin(C)) * sin(20°)

Since mB = mC, we have:

AC = (4 / sin(20°)) * sin(20°) = 4 centimeters

Answer 2

This is an isosceles triangle.
Draw a line from ∠A to the midpoint of segment BC and label that point M. This creates a 90 degree triangle AMC.

∠A for triangle ABC is 20 degrees. Since we bisected ∠A to create segment AM, then ∠A for triangle AMC is 10 degrees.

Since M is the midpoint of segment BC, then segment AC is 1/2 of segment BC (1/2 of 4 cm) = 2 cm.

Now you can use sin x = opposite/hypotenuse
sin ∠A = MC/AC
sin 10 = 2/AC
AC = 2/sin10
AC ≈ -3.68

Note: Since length cannot be negative, this cannot be a true triangle