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 :

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

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

c. side angle side. u shares the same sides