Question

3.
4.
5.
6.

Explanation:

Problem 3:

Step1: Identify trigonometric ratio

This is a right triangle with angle \(35^\circ\), opposite side \(7\), adjacent side \(x\). So we use \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\).
\(\tan(35^\circ)=\frac{7}{x}\)

Step2: Solve for \(x\)

Rearrange the formula: \(x = \frac{7}{\tan(35^\circ)}\)
Calculate \(\tan(35^\circ)\approx0.7002\), so \(x\approx\frac{7}{0.7002}\approx10\)

Step1: Identify trigonometric ratio

Right triangle, angle \(26^\circ\), adjacent side \(18\), hypotenuse \(x\). Use \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).
\(\cos(26^\circ)=\frac{18}{x}\)

Step2: Solve for \(x\)

Rearrange: \(x=\frac{18}{\cos(26^\circ)}\)
\(\cos(26^\circ)\approx0.8988\), so \(x\approx\frac{18}{0.8988}\approx20.03\)

Step1: Identify trigonometric ratio

Right triangle, angle \(19^\circ\), opposite side \(15\), hypotenuse \(x\). Use \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
\(\sin(19^\circ)=\frac{15}{x}\)

Step2: Solve for \(x\)

Rearrange: \(x = \frac{15}{\sin(19^\circ)}\)
\(\sin(19^\circ)\approx0.3256\), so \(x\approx\frac{15}{0.3256}\approx46.07\)

Answer:

\(x\approx10\)

Problem 4: