Finding missing parts

Question

Solve the right triangle below by finding all of its missing parts. Estimate your answer to one decimal place.

 

 

      H                      I

        x x x x x x x x 

        x                x

        x           x

 15.9 x        x 

        x59°x

         x

        K

Answer 1

You know the values of two of the angles, Rachel, so you should be able to easily find the value of the third angle. Remember that the angles of a triangle must add up to 180 degrees. You can make use of the various trigonometric functions (cosine, sine, tangent, etc.) to determine the length of the hypotenuse and the other leg of the right triangle.

 

For example, we can use the calculator to find tan 59°. Then, we can make use of the fact that tan = opposite side/adjacent side. We have the length of the adjacent side. It is 15.9. If we know the value of tan 59° and the value of the adjacent side, then it is easy to find the length of the opposite side.

 

Once you find the opposite side, then you can use the Pythagorean Theorem to find the length of the hypotenuse. Recall that:

 

a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse. If we know the lengths of any two sides, we can use the theorem to find the length of the remaining side.