Question

In right triangle $ABC,\angle C$ is a right angle, $AB=15$, and $BC=7$. Calculate the approximate measure of $\angle B$?

• A. ${25}^{\circ }$
• B. ${28}^{\circ }$
• C. ${62}^{\circ }$
• D. ${65}^{\circ }$
• E. ${82}^{\circ }$

Answer 1

Answer: (C)

${62}^{\circ }$

By using pythagoras theorem, we get

${AC}^2={AB}^2-{BC}^2$

$={15}^2-7^2$

$=225-49$

$=176$ ,

$\therefore AC=\sqrt{176}=13.26$
By sine rule, we get

$\frac{AC}{\sin B}=\frac{15}{1}$

$\therefore \sin B=\frac{AC}{15}=0.884$
$\therefore B={62}^o$