Question

Help a girl out pls n thx!!

Answer 1

The measure of angle C is 50 Degeree

To find the measure of angle C in triangle ABC, you can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

The Law of Cosines is expressed as:

`\[ c^2 = a^2 + b^2 - 2ab \cos(C) \]`

In this formula:

- c is the length of the side opposite angle C (BC in this case).

- a and b are the lengths of the other two sides (AB and AC, respectively).

- C is the measure of angle C.

Given the lengths:

- a = 6

- b = 7.5

- c = 6.5

Substitute these values into the Law of Cosines:

`\[ 6.5^2 = 6^2 + 7.5^2 - 2 \cdot 6 \cdot 7.5 \cos(C) \]`

Now, solve for cos(C):

`\[ 42.25 = 36 + 56.25 - 90 \cos(C) \]`
`\[ c^2 = a^2 + b^2 - 2ab \cos(C) \]`

`\[ 90 \cos(C) = 56.25 - 36 + 42.25 \]`

`\[ 90 \cos(C) = 62.5 \]`

`\[ \cos(C) = (62.5)/(90) \]\\ \cos(C) \approx 0.694`

Now, find the angle C by taking the inverse cosine (cos⁻¹) of 0.694:

`\[ C \approx \cos^(-1)(0.694) \]`

Using a calculator, you find that C is 50 degrees.

The probable question may be:

In triangle ABC Side Ab=6, BC=6.5,AC=7.5 What is the measure of angle C?

A. 50 degree

B. 60 degree

C. 77 degree

D. 82 degree

Answer 2

The answer is option A.

50 degrees

Explanation:

To find angle C we use the cosine rule

That's

AB² = AC ² + CB ² - 2(AC)(CB)cos C

AC = 7.5

AB = 6

CB = 6.5

6² = 7.5² + 6.5² - 2(7.5)(6.5)cosC

36 = 56.25 + 42.25 - 97.5cos C

36 - 98.5 = - 97.5 cos C

-62.5 = - 97.5 cos C

cos C = -62.5 / - 97.5

C = cos ^-1 25/39

C = 50.1

The final answer is

C = 50°

Hope this helps you.