In checking the angles of a section of a bridge support, an engineer finds the expression sin(2 cos-1 0.70). Write a paragraph explaining how the value of this expression can be found without the use of a calculator.

lol u had trouble on that one too huh

To find the value of the expression sin(2 cos-1 0.70) without using a calculator, we can use some basic trigonometric identities and properties. Let's break it down step by step:

1. We start with cos-1(0.70), which means we need to find the angle whose cosine is 0.70. Since cosine represents the ratio of the adjacent side to the hypotenuse in a right triangle, we can draw a right triangle where the adjacent side is 0.70 units long and the hypotenuse is 1 unit long.

2. To find the opposite side, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. Considering our triangle, we have 1^2 = (0.70)^2 + x^2, where x represents the opposite side.

3. Solving the equation, we get x = √(1^2 - 0.70^2) = √(1 - 0.49) = √0.51.

4. Now, we have cos-1(0.70) = θ, where cos(θ) = 0.70. Using the obtained value of x, we can write sin(θ) = √0.51 / 1 = √0.51.

5. Finally, we need to find sin(2θ). By using the double-angle formula for sine, sin(2θ) = 2sin(θ)cos(θ). Plugging in sin(θ) = √0.51 and cos(θ) = 0.70, we get sin(2θ) = 2(√0.51)(0.70) = 1.40√0.51.

Therefore, we have found that sin(2 cos-1 0.70) equals 1.40√0.51, which is the value of the given expression without a calculator.