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In a right triangle, angle A measures 20°. The side opposite angle A is 10 centimeters long. Approximately how long is the hypotenuse of the triangle? 3.4 centimeters 10.6 centimeters 27.5 centimeters 29.2 centimeters

Respuesta :

Given that the angle measure 20 and the side opposite to that angle measures 10 cm, suppose this is the height of the triangle, the hypotenuse
Such that
sin theta=opposite/hypotenuse
opposite=a=10 cm
sin 20=10/h
multiplying both sides by h we get
hsin20=10
hence;
h=10/sin20
h=29.24 cm
h=29.2 cm 

facundo3141592

By using a trigonometric relation, we will see that the hypotenuse measures 29.2 cm.

How to get the length of the hypotenuse?

Here we have a right triangle, and we know that one angle measures 20° and the opposite cathetus measures 10cm.

Here we can use the relation:

sin(a) = (opposite cathetus)/(hypotenuse)

In this case, we have:

  • a = 20°
  • opposite cathetus = 10cm
  • hypotenuse = H

Replacing that we get:

sin(20°) = 10cm/H

Solving for H we get:

H = 10cm/sin(20°) = 29.2 cm

If you want to learn more about right triangles, you can read:

https://brainly.com/question/2217700

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