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

Answer:

The measure of the side AB is 26 cm.

Step-by-step 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:

$sin\ \theta^{o}=\frac{Perpendicular}{Hypotenuse}$

Compute the length of side AB as follows:

$sin\ \theta^{o}=\frac{Perpendicular}{Hypotenuse}$

$sin\ 60^{o}=\frac{AB}{BC}\\\\0.866=\frac{AB}{30}\\\\AB=30\times 0.866\\\\AB=25.98\\\\AB\approx 26$

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