Question

1. solve for x using trig ratios a) 14 sin(33) = 7.62 c) 14 cos (33) = 11.74 b) 14 tan (33) = 11.74 17. solve for x using trig ratios a) 20 sin (57) = 16.77 b) 20 tan (57) = 30.80 c) 20 cos (57) = 10.89 18. a baseball diamond is a square with sides of 90 feet. how far will the ball have to be thrown from first base to reach third base?

Explanation:

Step1: Identify the right - triangle relationship for the first problem

In the first right - triangle with hypotenuse 14 and an angle of 33 degrees, and we want to find the side opposite the 33 - degree angle. The sine ratio is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. So, $x = 14\sin(33^{\circ})$.

Step2: Calculate the value of $x$ for the first problem

$x = 14\sin(33^{\circ})\approx14\times0.5446 = 7.6244\approx7.62$

Step3: Identify the right - triangle relationship for the second problem

In the second right - triangle with hypotenuse 20 and an angle of 57 degrees, and we want to find the side adjacent to the 57 - degree angle. The cosine ratio is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $x = 20\cos(57^{\circ})$.

Step4: Calculate the value of $x$ for the second problem

$x = 20\cos(57^{\circ})\approx20\times0.5446 = 10.892\approx10.89$

Step5: Solve the baseball - diamond problem

A baseball diamond is a square with side length $a = 90$ feet. The distance from first base to third base is the length of the diagonal of the square. Using the Pythagorean theorem $c^{2}=a^{2}+a^{2}$ (where $c$ is the diagonal and $a$ is the side - length of the square). Since $a = 90$ feet, $c=\sqrt{90^{2}+90^{2}}=\sqrt{2\times90^{2}}=90\sqrt{2}\approx90\times1.4142 = 127.278\approx127.28$ feet.

Answer:

1. For the first triangle, $x\approx7.62$
2. For the second triangle, $x\approx10.89$
3. For the baseball - diamond, the distance from first base to third base is approximately $127.28$ feet.