Question

Find the length x to the nearest whole number. A right triangle has a vertical leg of length x units, a base leg with a length of 330 units plus an unknown length, and a base angle of 28 degrees. The base leg is bisected by a line segment connecting to the vertical angle of the right triangle. The segment of the base leg that is closest to the 28 degree angle has length 330 units. The angle made from the segment of the base leg that is closest to the right angle and the bisecting line segment measures 56 degrees. 28 degrees 56 degrees x 330

Answer 1

Complete Question

The diagram for this question is shown on the first uploaded image

Answer:

The value of x is  $x = 274 \ unites$

Step-by-step explanation:

From the question we are told that

       The length of the vertical length is  $x$

      The length of the base leg is L = 330 + d units

      The length of the bisecting line segment is h

       The base angle is $\theta = 28^o$

       The angle between d and line segment is  $\theta_1 = 56^o$

For the first angle

         $Tan \theta_1 = \frac{x}{d}$

=>     $d = \frac{x}{Tan \theta _1}$

 For the whole big triangle

      $Tan \theta = \frac{x}{330 + d}$

=>     $d = \frac{x}{Tan \theta } -330$

So equating the both d

        $\frac{x}{Tan \theta _1} = \frac{x}{Tan \theta } -330$

Substitute values

        $\frac{x}{Tan (56)} = \frac{x}{Tan (28) } -330$

      $0.6745 x = 1.880x -330$

       $1.20549 x = 330$

       $x = 274 \ unites$