how to evaluate sin(a) when adj =4 and oposit side 10?
find hypot ... √(4^2 + 10^2)
sin = oposit / hypot = 10 / √(4^2 + 10^2)
since adj^2 + opp^2 = hyp^2
and sin = opp/hyp
in this case, sin(a) = 10/√(10^2+4^2) = 10/√116
To evaluate sin(a) when you have the length of the adjacent side and the length of the opposite side, you can use the formula of the sine trigonometric function:
sin(a) = opposite/hypotenuse
In this case, you are given the length of the adjacent side (adj = 4) and the length of the opposite side (opposite = 10). To find the hypotenuse, you can use the Pythagorean theorem.
The Pythagorean theorem states that the sum of the square of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the hypotenuse.
Using this, you can calculate the hypotenuse:
hypotenuse^2 = adjacent^2 + opposite^2
hypotenuse^2 = 4^2 + 10^2
hypotenuse^2 = 16 + 100
hypotenuse^2 = 116
hypotenuse ≈ √116
hypotenuse ≈ 10.77
Now that you have the lengths of the opposite side (10) and the hypotenuse (10.77), you can calculate sin(a) using the formula:
sin(a) = opposite/hypotenuse
sin(a) = 10/10.77
sin(a) ≈ 0.928
Therefore, sin(a) is approximately 0.928.