Question

a car travels 1.2 miles from point a to point b. the car then turns at point b and travels 1.8 miles to point c before heading back to point a. the distance from point point c to point a is 1.6 miles. if the cars path is represented by a triangle what angle turn

Answer 1

Since we are given with the three sides of the triangle and asked to determine the angle, we can use the cosine law.

                              b² = a² + c² - 2ac(cosB)

Substituting the known values,

                         (1.8)² = (2.4)² + (1.6)² - 2(2.4)(1.6)(cosB)

The value of B from the equation is 48.6°.

Answer 2

Answer:

B = 60.6 degree

Step-by-step explanation:

Side AB, c = 1.2 miles

Side BC, a = 1.8 miles

Side CA, b = 1.6 miles

Use Cosine rule to find the angle B.

$Cos B = \frac{a^{2}+c^{2}-b^{2}}{2ac}$

Putting the values of a, b and c

$Cos B = \frac{1.8^{2}+1.2^{2}-1.6^{2}}{2\times 1.8\times 1.2}$

$Cos B = \frac{3.24+1.44-2.56}{4.32}$

$Cos B = 0.491$

B = 60.6 degree