Question

10.3, 13.2, 14.2, 13.5, 12.4, 17, 12.9 (crossed out), x, 54°, 13.7, 4; find. cos n

Explanation:

Let's assume we are solving for \( x \) in the right - triangle with hypotenuse \( 17 \) and an angle of \( 54^{\circ} \), and \( x \) is adjacent to the \( 54^{\circ} \) angle.

Step 1: Recall the cosine formula

In a right - triangle, the cosine of an angle \( \theta \) is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). Here, \( \theta = 54^{\circ} \), the adjacent side to the angle \( 54^{\circ} \) is \( x \), and the hypotenuse is \( 17 \). So we have the formula \( \cos(54^{\circ})=\frac{x}{17} \).

Step 2: Solve for \( x \)

We can re - arrange the formula to solve for \( x \) by multiplying both sides of the equation by \( 17 \). So \( x = 17\times\cos(54^{\circ}) \).
We know that \( \cos(54^{\circ})\approx0.5878 \) (using a calculator). Then \( x=17\times0.5878 = 9.9926\approx10.0 \)

If we consider the other right - triangle (the one at the top with one leg \( 12.4 \) and we assume the other leg is \( x \) and the hypotenuse is related to the arrows, but since the triangle at the bottom with the \( 54^{\circ} \) angle is more clearly defined for a trigonometric solution, we will go with that.

Answer:

If we are solving the triangle with \( \theta = 54^{\circ} \) and hypotenuse \( 17 \), \( x\approx10.0 \) (If there are other triangles, more information about the given sides and what \( x \) represents is needed for a more accurate solution. For example, if the top - most right - triangle has one leg \( 12.4 \) and we assume the other leg is \( x \) and it's a right - triangle, we can use the Pythagorean theorem if we know the hypotenuse. But based on the given \( 54^{\circ} \) angle, \( x\approx10.0 \))