Respuesta :

mathmate
ABC is a right triangle right-angled at B.
AC is the hypotenuse, length 96cm
Angle C=30 degrees, therefore AB is the short leg opposite angle C.
sin(30)=opp/hyp=AB/AC=AB/96
=> 
AB=96sin(30)=96(1/2)=48 cm.

Answer:  The length of AB is 48 units.

Step-by-step explanation:  As shown in the attached figure below, ABC is a right-angled triangle where ∠B = 90°, AC = 96 cm and ∠C = 30°.

We are to find the length of side AB.

We know that

the sine of an acute angle in a right-angled triangle is the ratio of the perpendicular to hypotenuse of the triangle.

For angle C, the perpendicular is AB and hypotenuse is AC, the side opposite to the right angle.

Therefore, we get

[tex]\sin \angle C=\dfrac{perpendicular}{hypotenuse}\\\\\\\Rightarrow \sin30^\circ=\dfrac{AB}{AC}\\\\\\\Rightarrow \dfrac{1}{2}=\dfrac{AB}{96}\\\\\\\Rightarrow AB=\dfrac{96}{2}\\\\\Rightarrow AB=48.[/tex]

Thus, the length of AB is 48 units.

Ver imagen ColinJacobus

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