Question

Find the missing length indicated. A) 48 B) 36 C) 100 D) 64

Answer 1

Answer:

Option D) 64

Step-by-step explanation:  

see the attached figure with letters to better understand the problem

In the right triangle BCD find BC

Applying the Pythagoras Theorem

$BC^{2}=48^{2}+36^{2}\\BC^{2}=3,600\\BC=60\ units$

In the right triangle ABC

$cos(C)=BC/AC$

substitute the values  

$cos(C)=60/(x+36)$ -------> equation A

In the right triangle BDC

$cos(C)=CD/BC$

substitute the values

$cos(C)=36/60$ -------> equation B

equate equation A and equation B

$60/(x+36)=36/60\\ \\(x+36)*36=60*60\\ \\36x+1,296=3,600\\ \\36x=3,600-1,296\\ \\36x=2,304\\ \\x=64\ units$