A triangle has sides of length 5, 8, and 10. What is the measure of its largest angle?
1 answer:
We'll use the Law of Cosines
We'll call
side a = length 5
side b = length 8
side c = length 10
and their corresponding angles as A, B and C
"C" would be the largest angle
cos (C) = (a^2 + b^2 - c^2) / 2 * a * b
cos (C) = (5^2 + 8^2 - 10^2) / 2 * 5 * 8
cos (C) = 25 + 64 -100 / 80
cos (C) = -11 / 80
cos (C) = <span> <span> <span> -0.1375 </span> </span> </span>
arc cosine ( <span> <span> <span> -0.1375 </span> </span> </span> ) = 97.903 Degrees
The largest angle is 97.903 Degrees
We'll call
side a = length 5
side b = length 8
side c = length 10
and their corresponding angles as A, B and C
"C" would be the largest angle
cos (C) = (a^2 + b^2 - c^2) / 2 * a * b
cos (C) = (5^2 + 8^2 - 10^2) / 2 * 5 * 8
cos (C) = 25 + 64 -100 / 80
cos (C) = -11 / 80
cos (C) = <span> <span> <span> -0.1375 </span> </span> </span>
arc cosine ( <span> <span> <span> -0.1375 </span> </span> </span> ) = 97.903 Degrees
The largest angle is 97.903 Degrees
You might be interested in
For the triangle ABC use the sine theorem:
.
1. From you have
.
2. From you have
.
3. From you have
.
4. From you have
.
5. From you have
.
6. From you have
.