Question

worksheet 4 date___________ period
find the missing side. round to the nearest tenth. show work. box the final answer to receive
credit.
1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

Explanation:

Step1: Identify the triangle type (right triangle) and trigonometric ratios (sine, cosine, tangent)

For a right triangle, \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\), \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}\)

Step2: Solve problem 1:

Given: angle \(33^\circ\), adjacent side \(= 14\), opposite side \(= x\)
Use \(\tan(33^\circ)=\frac{x}{14}\)
\(x = 14\times\tan(33^\circ)\)
\(\tan(33^\circ)\approx0.6494\)
\(x\approx14\times0.6494\approx9.1\)

Step3: Solve problem 2:

Given: hypotenuse \(= 12\), angle \(58^\circ\), opposite side \(= x\)
Use \(\sin(58^\circ)=\frac{x}{12}\)
\(x = 12\times\sin(58^\circ)\)
\(\sin(58^\circ)\approx0.8480\)
\(x\approx12\times0.8480\approx10.2\)

Step4: Solve problem 3:

Given: angle \(32^\circ\), adjacent side \(= 12\), opposite side \(= x\)
Use \(\tan(32^\circ)=\frac{x}{12}\)
\(x = 12\times\tan(32^\circ)\)
\(\tan(32^\circ)\approx0.6249\)
\(x\approx12\times0.6249\approx7.5\)

Step5: Solve problem 4:

Given: angle \(58^\circ\), adjacent side \(= 11\), opposite side \(= x\)
Use \(\tan(58^\circ)=\frac{x}{11}\)
\(x = 11\times\tan(58^\circ)\)
\(\tan(58^\circ)\approx1.6003\)
\(x\approx11\times1.6003\approx17.6\)

Step6: Solve problem 5:

Given: angle \(28^\circ\), adjacent side \(= 18\), opposite side \(= x\)
Use \(\tan(28^\circ)=\frac{x}{18}\)
\(x = 18\times\tan(28^\circ)\)
\(\tan(28^\circ)\approx0.5317\)
\(x\approx18\times0.5317\approx9.6\)

Step7: Solve problem 6:

Given: hypotenuse \(= 11\), angle \(32^\circ\), adjacent side \(= x\)
Use \(\cos(32^\circ)=\frac{x}{11}\)
\(x = 11\times\cos(32^\circ)\)
\(\cos(32^\circ)\approx0.8480\)
\(x\approx11\times0.8480\approx9.3\)

Step8: Solve problem 7:

Given: adjacent side \(= 18\), angle \(67^\circ\), opposite side \(= x\)
Use \(\tan(67^\circ)=\frac{x}{18}\)
\(x = 18\times\tan(67^\circ)\)
\(\tan(67^\circ)\approx2.3559\)
\(x\approx18\times2.3559\approx42.4\)

Step9: Solve problem 8:

Given: adjacent side \(= 13\), angle \(61^\circ\), opposite side \(= x\)
Use \(\tan(61^\circ)=\frac{x}{13}\)
\(x = 13\times\tan(61^\circ)\)
\(\tan(61^\circ)\approx1.8040\)
\(x\approx13\times1.8040\approx23.5\)

Step10: Solve problem 9:

Given: angle \(47^\circ\), adjacent side \(= 13\), opposite side \(= x\)
Use \(\tan(47^\circ)=\frac{x}{13}\)
\(x = 13\times\tan(47^\circ)\)
\(\tan(47^\circ)\approx1.0724\)
\(x\approx13\times1.0724\approx13.9\)

Step11: Solve problem 10:

Given: angle \(42^\circ\), opposite side \(= 19\), adjacent side \(= x\)
Use \(\tan(42^\circ)=\frac{19}{x}\)
\(x=\frac{19}{\tan(42^\circ)}\)
\(\tan(42^\circ)\approx0.9004\)
\(x\approx\frac{19}{0.9004}\approx21.1\)

Answer:

1. \(\boxed{9.1}\)
2. \(\boxed{10.2}\)
3. \(\boxed{7.5}\)
4. \(\boxed{17.6}\)
5. \(\boxed{9.6}\)
6. \(\boxed{9.3}\)
7. \(\boxed{42.4}\)
8. \(\boxed{23.5}\)
9. \(\boxed{13.9}\)
10. \(\boxed{21.1}\)