skyknight
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in right triangle ABC, C is the right angle. Given measure of angle A = 40 degrees and a =6, which of the following are the lengths of the remaining two side, rounded to the nearest tenth?

Respuesta :

wolf1728
tan 40° = 6 / AC
AC = 6 / tan 40°
AC = 6 / .8391
AC = 7.15

AB² = 6² + 7.15²
AB² = 36 + 51.123
AB² = 87.12
AB = 9.33

 
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By using trigonometric relations we will see that the other two sides are:

b = 7.2

c = 9.3

How do find the other two sides for a right triangle?

We have the triangle ABC, we know that:

  • A = 40°
  • C = 90°
  • a = 6.

a is the opposite cathetus to angle A, c would be the hypotenuse (because it is the opposite side to angle C) and b is the adjacent cathetus to angle A.

Using the trigonometric relations:

  • tan(θ) = (opposite cathetus)/(adjacent cathetus).
  • sin(θ) = (opposite cathetus)/(hypotenuse).

We can find the two missing sides:

Tan(40°) = 6/b

b = 6/Tan(40°) = 7.2

Sin(40°) = 6/c

c = 6/Sin(40°) = 9.3

These are the other two sides of the right triangle.

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

https://brainly.com/question/2217700

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