Let's go through each of the tasks step by step, using the approach shown in Example 6.

Task 6

Given:

• Side $b = 12$ m (adjacent to $\angle 60^\circ$)
• $\angle A = 60^\circ$

a) Find the measure of the hypotenuse (side $c$):

We use the cosine rule: $\cos 60^\circ = \frac{b}{c}$ $c = \frac{b}{\cos 60^\circ} = \frac{12}{0.5} = 24 \text{ m}$

The example result was incorrect. Let's continue fixing.

b) Find the measure of side $a$:

We use the tangent rule: $\tan 60^\circ = \frac{a}{b}$ $a = b \tan 60^\circ = 12 \cdot 1.732 = 20.8 \text{ m}$

But given wrong earlier. We continue correcting.Now, let's correct and complete each question.

Question 6

Given:

• $b = 5.5$ m
• $\angle A = 66^\circ$

a) Find the measure of the hypotenuse (side $c$):

$\cos 66^\circ = \frac{b}{c} \Rightarrow c = \frac{5.5}{\cos 66^\circ}$ $c \approx \frac{5.5}{0.4067} = 13.5 \text{ m}$

b) Find the measure of side $a$:

$\tan 66^\circ = \frac{a}{b} \Rightarrow a = b \tan 66^\circ$ $a = 5.5 \cdot 2.246 = 12.4 \text{ m}$

Question 7

Given:

• $\angle C = 70^\circ$
• $a = 35.5$ cm

a) Find side $b$:

$\tan 70^\circ = \frac{a}{b} \Rightarrow b = \frac{a}{\tan 70^\circ}$ $b = \frac{35.5}{2.747} \approx 12.9 \text{ cm}$

b) Find hypotenuse $c$:

$\sin 70^\circ = \frac{a}{c} \Rightarrow c = \frac{a}{\sin 70^\circ}$ $c = \frac{35.5}{0.9397} \approx 37.8 \text{ cm}$

Question 8

Given:

• $c = 100$ m