The length of side BC to one decimal place is 14.9.
To find the length of side BC in the given right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore, we have:
BC² = CA² + AB²
Substituting the given values, we get:
BC² = 10² + (AB*sin(A))²
Since angle A is given as 42 degrees, we can use the sine function to find sin(A):
sin(A) = sin(42) = 0.6691
Substituting this value, we get:
BC² = 100 + (AB*0.6691)²
Simplifying, we get:
BC² = 100 + 0.4472*AB²
We are also given that angle C is 90 degrees, so we know that BC is the hypotenuse. Therefore, we can solve for BC by taking the square root of both sides:
BC = sqrt(100 + 0.4472*AB²)
Substituting the given values, we get:
BC = (100 + 0.4472*(10²)*(sin(42))²) ≈ 14.9
Therefore, the length of side BC to one decimal place is 14.9.