Question

calculate the value of ab, correct to 2 decimal places.

Explanation:

Step1: Find length of AC in right - triangle ADC

In right - triangle ADC, $\angle D = 90^{\circ}$, $AD = 10$ and $\angle DAC=35^{\circ}$. We use the cosine function $\cos\theta=\frac{adjacent}{hypotenuse}$. Here, $\cos35^{\circ}=\frac{AD}{AC}$, so $AC=\frac{AD}{\cos35^{\circ}}$. Since $AD = 10$, then $AC=\frac{10}{\cos35^{\circ}}\approx\frac{10}{0.8192}\approx12.21$.

Step2: Find length of AB in right - triangle ABC

In right - triangle ABC, $\angle B = 90^{\circ}$, $\angle CAB = 20^{\circ}$ and we know $AC$. We use the cosine function again. $\cos\angle CAB=\frac{AB}{AC}$, so $AB = AC\times\cos20^{\circ}$. Substituting the value of $AC\approx12.21$, we get $AB\approx12.21\times0.9397\approx11.47$.

Answer:

$11.47$