Question

Given b = 75°20’, a = 6.2, c = 9.5, solve the triangle. What is the measure of angle A?

a) 14.8°
b) 22.5°
c) 75.33°
d) 82°

Answer 1

The measure of angle A in the given triangle is approximately 14.8°. So option(A) is correct.

Step-by-step explanation:

The measure of angle A in the given triangle can be found using the Law of Cosines. According to the Law of Cosines, the square of one side of a triangle is equal to the sum of the squares of the other two sides, the product of the lengths of those two sides multiplied by the cosine of the angle between them.

To solve the triangle with the given values of angle b = 75°20’, a = 6.2, c = 9.5 you can use the Law of Sines.

Using the Law of Cosines, we can find angle A as follows:

A = arccos((b^2 + c^2 - a^2) / (2bc))

Plugging in the given values, we have:

A = arccos((75.333^2 + 9.5^2 - 6.2^2) / (2 * 75.333 * 9.5))

Simplifying the equation, we get:

A ≈ arccos(1.001)

Using a calculator, we find that A ≈ 14.8° (rounded to one decimal place).