Question

1. x 16 28° 12) 13 28° x

Explanation:

Problem 11:

Step 1: Identify the trigonometric ratio

We have a right triangle with an angle of \(28^\circ\), the opposite side to the angle is \(16\), and \(x\) is the adjacent side. So we use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(28^\circ)=\frac{16}{x}\)

Step 2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{16}{\tan(28^\circ)}\)
Calculate \(\tan(28^\circ)\approx0.5317\)
Then \(x=\frac{16}{0.5317}\approx30.1\) (rounded to one decimal place)

Step 1: Identify the trigonometric ratio

We have a right triangle with hypotenuse \(13\), angle \(28^\circ\), and \(x\) is the adjacent side. So we use the cosine function: \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\)
\(\cos(28^\circ)=\frac{x}{13}\)

Step 2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = 13\times\cos(28^\circ)\)
Calculate \(\cos(28^\circ)\approx0.8829\)
Then \(x = 13\times0.8829\approx11.5\) (rounded to one decimal place)

Answer:

\(x\approx30.1\)

Problem 12: