Question

a missing side practice
the tenths place. triangles may not be drawn to scale.
2.
5
34°
x
4.
7
47°
x

Explanation:

Step1: Use trigonometric ratio for problem 2

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 34^{\circ}\), adjacent side \(=5\), and opposite side \(=x\). So \(\tan34^{\circ}=\frac{x}{5}\).

Step2: Solve for \(x\) in problem 2

We know that \(\tan34^{\circ}\approx0.6745\). Then \(x = 5\times\tan34^{\circ}\approx5\times0.6745 = 3.4\).

Step1: Use trigonometric ratio for problem 4

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 47^{\circ}\), hypotenuse \(=7\), and opposite side \(=x\). So \(\sin47^{\circ}=\frac{x}{7}\).

Step2: Solve for \(x\) in problem 4

We know that \(\sin47^{\circ}\approx0.7314\). Then \(x=7\times\sin47^{\circ}\approx7\times0.7314 = 5.1\).

Answer:

For problem 2: \(x\approx3.4\)
For problem 4: \(x\approx5.1\)