Question

Em um triangulo retangulo abc EM QUE A HIPOTENUSA BC mede 30cm sabe-se que o seno do angulo oposto ao lado ab mede 0,6 desse modo conclui-se que a medida do lado Ab desse triangulo mede

Answer 1

The measure of the side AB is 26 cm.

Explanation:

The question is:

In a triangle ABC the hypotenuse BC measures 30 cm, it is known that the angle of the opposite angle to the side AB, measures 60°, therefore it is concluded that as side AB the triangle measures ?

Solution:

Consider the triangle ABC.

The side BC is defined as a hypotenuse. This implies that the triangle ABC is a right angled triangle.

The angle A measures 90° and the angle C measures 60°.

The hypotenuse length is 30 cm.

According to the trigonometric identities for right angled triangle:

`sin\ \theta^(o)=(Perpendicular)/(Hypotenuse)`

Compute the length of side AB as follows:

`sin\ \theta^(o)=(Perpendicular)/(Hypotenuse)`

`sin\ 60^(o)=(AB)/(BC)\\\\0.866=(AB)/(30)\\\\AB=30* 0.866\\\\AB=25.98\\\\AB\approx 26`

Thus, the measure of the side AB is 26 cm.