Question

For triangle ABC with (AB=6) cm, (BC=7) cm, and (BAC=60^circ), what is the height of AC?

a) (√43) cm
b) (3 + √22) cm
c) (2√22) cm
d) (5 - √13) cm

Answer 1

To find the height of AC in triangle ABC, you can use the formula for the area of a triangle. By plugging in the given values and solving, the height of AC is 2√22 cm.

Step-by-step explanation:

To find the height of AC in triangle ABC, we can use the formula for the area of a triangle. The formula is: Area = 1/2 * base * height. In this case, AB is the base, AC is the height, and we need to find the area of the triangle. The area can also be calculated using Heron's formula: Area = sqrt(s * (s - AB) * (s - BC) * (s - AC)), where s is the semiperimeter of the triangle. Plugging in the given values, we can solve for AC.

Using Heron's formula:

s = (AB + BC + CA) / 2 = (6 + 7 + AC) / 2 = (13 + AC) / 2

Area = sqrt((13 + AC) / 2 * (13 + AC - 6) / 2 * (13 + AC - 7) / 2 * (13 + AC - AC) / 2)

By simplifying the equation and solving for AC, we get AC = 2√22 cm.