The two sides of the triangle are 1.3 and 42.5, the angle between them is 100 °.

The two sides of the triangle are 1.3 and 42.5, the angle between them is 100 °. Calculate the third side of the triangle using the cosine solution theorem.

We write the formula of the cosine theorem:
A ^ 2 = B ^ 2 + C ^ 2 – 2 * B * C * cos <(B, C).
According to the Bradis table, we find the value for cos 100 °.
cos 100 ° ~ -0.17.
B = 1.3; C = 42.5 – by condition.
Substitute the data into the above formula and find the square of the third side of this triangle:
A ^ 2 = B ^ 2 + C ^ 2 – 2 * B * C * cos 100 ° = (1.3) ^ 2 + (42.5) ^ 2 – 2 * 1.3 * 42.5 * (- 0.17).
Let’s square the numbers:
1.69 + 1806.25 – 2 * 1.3 * 42.5 * (-0.17).
Let’s multiply all the factors in the part of the subtracted from each other:
1.69 + 1806.25 – 2.6 * (-7.225);
1.69 + 1806.25 – (-18.785);
Let’s add the numbers in the part to be reduced and open the brackets:
1807.94 + 18.785 = 1826.725.
A ^ 2 = 1826.725;
Find the root of the given number:
A = 42.7.
Answer: 42.7.