how to evaluate sin(a) when adj =4 and oposit side 10?
sketch a right triangle, two sides 4, 10.
then the hypotenuse is c^2=4^2+10^2
that works out to be 116.
so SinA=10/sqrt(116)
anna: you already asked this, and got an answer before you posted this. Is there something you don't understand about it? We don't have crystal balls here.
To evaluate sin(a) when given the lengths of the adjacent and opposite sides of a right triangle, you can use the following steps:
Step 1: Understand the Trigonometric Ratio
In a right triangle, the sine of an angle (a) is equal to the length of the opposite side divided by the length of the hypotenuse. The hypotenuse is the side opposite the right angle and is not given in this case. However, you can still proceed by using the given lengths.
Step 2: Use the Pythagorean Theorem
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the given sides are the adjacent side (4) and the opposite side (10). We can use this theorem to find the length of the hypotenuse.
Using the Pythagorean Theorem:
hypotenuse^2 = adjacent^2 + opposite^2
hypotenuse^2 = 4^2 + 10^2
hypotenuse^2 = 16 + 100
hypotenuse^2 = 116
Step 3: Find the Length of the Hypotenuse
To find the length of the hypotenuse, take the square root of both sides of the equation:
√(hypotenuse^2) = √116
hypotenuse ≈ 10.77 (rounded to two decimal places)
Step 4: Evaluate sin(a)
Now that you know the lengths of the adjacent side (4) and the hypotenuse (10.77), you can compute sin(a):
sin(a) = opposite / hypotenuse
sin(a) = 10 / 10.77
sin(a) ≈ 0.928 (rounded to three decimal places)
Therefore, sin(a) is approximately 0.928 when the adjacent side is 4 and the opposite side is 10.