Question

DESDE LA PARTE ALTA DE UN MURO DE 8M DE ALTURA SE OBSERVA LAS PARTE BAJA Y ALTA DE UN EDIFICIO CON ANGULOS DE ELEVACION Y DEPRESION DE 37 Y 45 RESPECTIVAMENTE. CALCULA LA ALTURA DEL EDIFICIO A.18 B.14 C.12 D.24 E.16

Answer 1

Answer:

The height of the building is approximately 18 meters.

Step-by-step explanation:

The question is:

FROM THE HIGH PART OF A WALL OF 8M HEIGHT, YOU CAN SEE THE LOW AND HIGH PART OF A BUILDING WITH ELEVATION AND DEPRESSION ANGLES OF 37° AND 45° RESPECTIVELY. CALCULATE THE HEIGHT OF THE BUILDING A.18 B.14 C.12 D.24 E.16

Solution:

Consider the diagram below.

Consider the triangle ABC.

Compute the value of y as follows:

$tan\ 37^{o}=\frac{AB}{BC}$

  $0.754=\frac{8}{y}$

        $y=\frac{8}{0.754}$

           $=10.61\\\approx 11$

Thus, the length of side AD is also 11 meters.

Now consider the triangle AED.

Compute the value of x as follows:

$tan\ 45^{o}=\frac{AE}{ED}$

        $1=\frac{11}{x}$

        $x=11$

Then the height of the building is:

$\text{Height of the Building}=x+8$

                                 $=11+8\\=19$

From the options provided it can be concluded that the height of the building is approximately 18 meters.