Question

section b find the missing angles or lengths x.

Explanation:

Step1: Recall trigonometric ratios

For right - angled triangles, we use $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Solve for (1)

We know two sides of the right - angled triangle. $\tan x=\frac{5}{11}$, so $x = \arctan(\frac{5}{11})\approx24.44^{\circ}$.

Step3: Solve for (2)

$\tan x=\frac{0.21}{0.7}=0.3$, so $x=\arctan(0.3)\approx16.70^{\circ}$.

Step4: Solve for (3)

$\tan62^{\circ}=\frac{6.4}{x}$, then $x=\frac{6.4}{\tan62^{\circ}}\approx3.39$ cm.

Step5: Solve for (4)

First, convert 1.5 cm to 15 mm. $\cos x=\frac{15}{27}=\frac{5}{9}$, so $x=\arccos(\frac{5}{9})\approx56.27^{\circ}$.

Step6: Solve for (5)

$\tan13^{\circ}=\frac{2.3}{x}$, then $x = \frac{2.3}{\tan13^{\circ}}\approx9.97$ cm.

Step7: Solve for (6)

First, convert 8 m to 800 cm. $\sin x=\frac{620}{800}=0.775$, so $x=\arcsin(0.775)\approx50.87^{\circ}$.

Answer:

(1) $x\approx24.44^{\circ}$
(2) $x\approx16.70^{\circ}$
(3) $x\approx3.39$ cm
(4) $x\approx56.27^{\circ}$
(5) $x\approx9.97$ cm
(6) $x\approx50.87^{\circ}$