Question

If triangle abc, a=3, b=5 and c=7. Find the measure of angle b

Answer 1

β = arccos((a^2 + c^2 - b^2)/(2·a·c))

β = arccos((3^2 + 7^2 - 5^2)/(2·3·7)) = 38.21°

Answer 2

b = 38.22

Explanation:

In the given triangle ABC, a = 3, b = 5 and c = 7 is given.

We have to find the measure of angle b.

To get the measure of any angle we will apply cosine rule in the triangle.

b² = a² + c² - 2ac(cosb)

5² = 3² + 7² - 2×3×7×cosb

25 = 9 + 49 - 42×cosb

25 = 58 - 42cosb

-42cosb = 25 - 58 = -33

cosb =
`(33)/(42)`

cosb = 0.7856

`b= cos^(-1)(0.7856)`

b = 38.22

b = 38.22 is the correct answer.