zanaplen27
contestada

ABCD is a trapezoid (AD∥ BC). BC = 5 cm, m∠ACD = m∠ABC = 90°, m∠BAC = 30°. Find the length of AD (the picture is not drawn to scale).

ABCD is a trapezoid AD BC BC 5 cm mACD mABC 90 mBAC 30 Find the length of AD the picture is not drawn to scale class=

Respuesta :

calculista

Answer:

[tex]AD=20\ cm[/tex]  

Step-by-step explanation:

step 1

Find the length of AC

In the right triangle ABC

[tex]sin(<BAC)=\frac{BC}{AC}[/tex]

we have

[tex]m<BAC=30\°[/tex]

[tex]BC=5\ cm[/tex]

substitute and solve for AC

[tex]sin(30\°)=\frac{5}{AC}[/tex]

[tex]0.5=\frac{5}{AC}[/tex]  

[tex]AC=10\ cm[/tex]          

step 2

Find the length side AD

In the right triangle ACD

[tex]cos(<CAD)=\frac{AC}{AD}[/tex]

we have

[tex]m<CAD=90\°-30\°=60\°[/tex]

[tex]AC=10\ cm[/tex]

substitute and solve for AD

[tex]cos(60\°)=\frac{10}{AD}[/tex]

[tex]0.5=\frac{10}{AD}[/tex]

[tex]AD=20\ cm[/tex]  

Otras preguntas