Question

triangle abc has a right angle. angle bac is 25°. ac = 12.5cm. calculate the length of ab

Explanation:

Step1: Identify the trigonometric relation

In right - triangle $ABC$, $\cos\angle BAC=\frac{AB}{AC}$.

Step2: Rearrange the formula for $AB$

$AB = AC\times\cos\angle BAC$.

Step3: Substitute the given values

Given $AC = 12.5$ cm and $\angle BAC=25^{\circ}$, so $AB=12.5\times\cos25^{\circ}$.

Step4: Calculate the value

$\cos25^{\circ}\approx0.9063$, then $AB = 12.5\times0.9063=11.32875\approx11.33$ cm.

Answer:

$AB\approx11.33$ cm