Question

The angle of elevation of the top of a tower from a point A due south of the tower is $A B = d$, then the height of the tower is

• A. $\frac { d } { \sqrt { \tan ^ { 2 } \alpha - \tan ^ { 2 } \beta } }$
• B. $\frac { d } { \sqrt { \tan ^ { 2 } \alpha + \tan ^ { 2 } \beta } }$
• C. $\frac { d } { \sqrt { \cot ^ { 2 } \alpha + \cot ^ { 2 } \beta } }$
• D. $\frac { d } { \sqrt { \cot ^ { 2 } \alpha - \tan ^ { 2 } \beta } }$

Answer 1

Answer: (C)

$\frac { d } { \sqrt { \cot ^ { 2 } \alpha + \cot ^ { 2 } \beta } }$

Answer 2

$O B = h \cot \beta$

$O A = h \cot \alpha$

⇒ $h ^ { 2 } = \frac { d ^ { 2 } } { \cot ^ { 2 } \beta + \cot ^ { 2 } \alpha }$

⇒ $h = \frac { d } { \sqrt { \cot ^ { 2 } \beta + \cot ^ { 2 } \alpha } }$