Question

trigonometry
practice

1. solve for x rounded to one decimal place.

(a) sin 35° = x/8
(b) cos 70° = x/15
(c) tan 20° = 3/x
(d) sin 85° = 6/x
(e) cos 25° = 5/x

Explanation:

Part (A)

Step1: Isolate \( x \)

Multiply both sides by 8: \( x = 8 \sin 35^\circ \)

Step2: Calculate \( \sin 35^\circ \)

\( \sin 35^\circ \approx 0.5736 \)

Step3: Compute \( x \)

\( x = 8 \times 0.5736 \approx 4.6 \)

Step1: Isolate \( x \)

Multiply both sides by 15: \( x = 15 \cos 70^\circ \)

Step2: Calculate \( \cos 70^\circ \)

\( \cos 70^\circ \approx 0.3420 \)

Step3: Compute \( x \)

\( x = 15 \times 0.3420 \approx 5.1 \)

Step1: Rearrange the equation

\( x = \frac{3}{\tan 20^\circ} \)

Step2: Calculate \( \tan 20^\circ \)

\( \tan 20^\circ \approx 0.3640 \)

Step3: Compute \( x \)

\( x = \frac{3}{0.3640} \approx 8.2 \)

Answer:

\( x \approx 4.6 \)

Part (B)