Question

use the following diagram to answer question 5.

1. a. outline the steps you would take to find side f.

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b. solve for side d. round to one decimal place.

Explanation:

Step1: Find side \(e\)

In the right - triangle with height \(51\) and angle \(12^{\circ}\), use the trigonometric relation \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan(12^{\circ})=\frac{51}{e}\), so \(e = \frac{51}{\tan(12^{\circ})}\).

Step2: Find side \(f\)

In the right - triangle with side \(e\) and angle \(75^{\circ}\), use the trigonometric relation \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\sin(75^{\circ})=\frac{e}{f}\), so \(f=\frac{e}{\sin(75^{\circ})}\).

Step1: Solve for side \(d\)

In the right - triangle with height \(51\) and angle \(25^{\circ}\), use the trigonometric relation \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
We know that \(\sin(25^{\circ})=\frac{51}{d}\).

Step2: Rearrange the formula for \(d\)

$$d=\frac{51}{\sin(25^{\circ})}$$

$$d=\frac{51}{0.4226}$$

$$d\approx120.7$$

Answer:

a. First, find \(e=\frac{51}{\tan(12^{\circ})}\), then find \(f = \frac{e}{\sin(75^{\circ})}\).
b. \(d\approx120.7\)