contestada

A truck parked on the street is 56 m from the base of the apartment building on the right. The angle of elevation from the truck to the top of the building is 40°. The parked truck is 49 m from the base of the apartment building on the left. The angle of elevation from the truck to the top of that building is 50°. Which building is taller?

Respuesta :

isyllus

Answer:

Building to the left is taller.

Step-by-step explanation:

Kindly refer to the attached diagram for the given dimensions.

[tex]\triangle ABR, \triangle PQR[/tex]

AB and PQ be the two buildings.

The car be parked at point R.

[tex]\angle ARB = 50^\circ\ and \\\angle PRQ = 40^\circ[/tex]

Distance of R from building bases:

BR = 49 m

QR = 56 m

Let us use tangent in [tex]\triangle PQR:[/tex]

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan40 = \dfrac{h_1}{56}\\\Rightarrow h_1 = 56 \times 0.839 \\\Rightarrow h_1 \approx 47\ m[/tex]

Let us use tangent in [tex]\triangle PQR:[/tex]

[tex]tan\theta = \dfrac{Perpendicular}{Base}[/tex]

[tex]tan50 = \dfrac{h_2}{49}\\\Rightarrow h_2 = 49 \times 1.19 \\\Rightarrow h_2 \approx 58.4\ m[/tex]

So, building to the left is taller.

Ver imagen isyllus

Otras preguntas