Question

Using the triangle pictured, find the measure of angle C. Round your answer to the nearest tenth.

Answer 1

Explanation:

already calculated A=53

B=72

C=180-(53+72)=180-125=55°

Answer 2

The sine of angle C is approximately 0.799, and the measure of angle C is 53.0° when rounded to the nearest tenth. therefore, option B is correct

To find the measure of angle
`\( C \)` in triangle
`\( ABC \)`, we will use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. That is:

`\[ (a)/(\sin(A)) = (b)/(\sin(B)) = (c)/(\sin(C)) \]`

Where a,b and c are the lengths of the sides of the triangle, and A,B and C are the angles opposite those sides, respectively.

Given:

`\( AB = 2.5 \)`

`\( BC = 2.1 \)`

`\( \angle B = 72° \)`

We want to find
`\( \angle C \).`

Using the Law of Sines, we can set up the following equation:

`\[ (AB)/(\sin(B)) = (BC)/(\sin(C)) \]`

`\[ (2.5)/(\sin(72°)) = (2.1)/(\sin(C)) \]`

Solving for \( \sin(C) \), we get:

`\[ \sin(C) = (2.1 \cdot \sin(72°))/(2.5) \]`

Let's calculate the value of
`\( \sin(C) \)`and then find
`\( \angle C \)` by taking the inverse sine.

The sine of angle C is approximately 0.799, and the measure of angle C is 53.0° when rounded to the nearest tenth.