Trigonometric Equations Question 100
Question: If the two angle on the base of a triangle are $ {{( 22\frac{1}{2} )}^{o}} $ and $ {{( 112\frac{1}{2} )}^{o}} $ , then the ratio of the height of the triangle to the length of the base is
[MP PET 1993; Pb CET 2002]
Options:
A) 1 : 2
B) 2 : 1
C) 2 : 3
D) 1: 1
Show Answer
Answer:
Correct Answer: A
Solution:
- In $ \Delta ACD,,\frac{h}{\sin {{67.5}^{o}}}=\frac{AC}{\sin 90^{o}} $
$ \Rightarrow \frac{h}{AC}=\sin {{67.5}^{o}} $ ….(i) In $ \Delta ABC,,\frac{AC}{\sin {{22.5}^{o}}}=\frac{x}{\sin 45^{o}}\Rightarrow \frac{AC}{x}=\sqrt{2}\sin {{22.5}^{o}} $ …..(ii) From (i) and (ii), $ \frac{h}{x}=\frac{1}{2} $ .
BETA
