Given: abc is a right triangle with right angle c. ac=15 centimeters and m∠a=40∘ . what is bc ? enter your answer, rounded to the nearest tenth, in the box

In order to answer this question, the figure in the first picture will be helpful to understand what a right triangle is. Here, a right angle refers to .

However, if we want to solve the problem we have to know certain things before:

In the second figure is shown a general right triangle with its three sides and another given angle, we will name it :

The side opposite to the right angle is called The Hypotenuse (h) The side opposite to the angle is called the Opposite (O) The side next to the angle is called the Adjacent (A)

So, going back to the triangle of our question (first figure):

The Hypotenuse is AB The Opposite is BC The Adjacent is AC

Now, if we want to find the length of each side of a right triangle, we have to use the Pythagorean Theorem and Trigonometric Functions:

Pythagorean Theorem

   (1)  

Trigonometric Functions (here are shown three of them):

Sine:    (2)

Cosine:    (3)

Tangent:   (4)

In this case the function that works for this problem is cosine (3), let’s apply it here:

   

   (5)

And we will use the Pythagorean Theorem to find the hypotenuse, as well:

   

   (6)

  (7)

Substitute (7) in (5):

   

Then clear BC, which is the side we want:

Finally is approximately 13 cm

Logical equivalent of the give question is its contrapositive

It’s 24.6 after you round to the nearest tenths the answer should be 25.0