Question

solving right triangles
date: 2/9/20
find the missing side. round to the nearest tenth.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Step1: Use tangent for angle 72°

$\tan(72^\circ) = \frac{x}{6}$
$x = 6 \times \tan(72^\circ) \approx 6 \times 3.078 = 18.5$

Step2: Use tangent for angle 78°

$\tan(78^\circ) = \frac{8}{x}$
$x = \frac{8}{\tan(78^\circ)} \approx \frac{8}{4.705} \approx 1.7$

Step3: Use tangent for angle 24°

$\tan(24^\circ) = \frac{x}{12}$
$x = 12 \times \tan(24^\circ) \approx 12 \times 0.445 = 5.3$

Step4: Use tangent for angle 37°

$\tan(37^\circ) = \frac{x}{12}$
$x = 12 \times \tan(37^\circ) \approx 12 \times 0.754 = 9.0$

Step5: Use tangent for angle 40°

$\tan(40^\circ) = \frac{14}{x}$
$x = \frac{14}{\tan(40^\circ)} \approx \frac{14}{0.839} \approx 16.7$

Step6: Use tangent for angle 51°

$\tan(51^\circ) = \frac{x}{14}$
$x = 14 \times \tan(51^\circ) \approx 14 \times 1.235 = 17.3$

Step7: Use tangent for angle 60°

$\tan(60^\circ) = \frac{x}{16}$
$x = 16 \times \tan(60^\circ) = 16 \times \sqrt{3} \approx 16 \times 1.732 = 27.7$

Step8: Use tangent for angle 15°

$\tan(15^\circ) = \frac{10}{x}$
$x = \frac{10}{\tan(15^\circ)} \approx \frac{10}{0.268} \approx 37.3$

Answer:

1. $18.5$
2. $1.7$
3. $5.3$
4. $9.0$
5. $16.7$
6. $17.3$
7. $27.7$
8. $37.3$