Two men on either side of a temple of 30 meters high observe its top at the angles of elevation and respectively.

Question

Two men on either side of a temple of 30 meters high observe its top at the angles of elevation α and β respectively. (as shown in the figure above). The distance between the two men is 40√3 meters and the distance between the first person A and the temple is 30√3 meters. Based on the above information answer the following:

1. ∠CAB = α =

a. sin−1 (\(\cfrac{2}{\sqrt3}\))

b. sin−1 (\(\cfrac12\))

c. sin−1 (2)

d. sin−1 (\(\cfrac{\sqrt3}2\))

2. ∠CAB = α =

a. cos−1 (\(\cfrac15\))

b. cos−1 (\(\cfrac25\))

c. cos−1 (\(\cfrac{\sqrt3}2\))

d. cos−1 (\(\cfrac45\))

3. ∠BCA = β =

a. tan−1 (\(\cfrac12\))

b. tan−1 (2)

c. tan−1 ( \(\cfrac1{\sqrt3}\) )

d. tan−1 (\({\sqrt3}\))

4. ∠ABC =

a. \(\cfrac\pi4\) 

b. \(\cfrac\pi6\) 

c. \(\cfrac\pi2\)

d.\(\cfrac\pi3\) 

5. Domain and Range of cos⁻¹ x =

a. ( −1, 1 ), (0, π)

b. [ −1, 1 ], (0, π)

c. [ −1, 1 ], [0, π]

d. ( −1, 1 ) , [− \(\cfrac\pi2\) , \(\cfrac\pi2\) ]

Answer 1

1. ( b ) sin⁻¹ ( \(\cfrac12\) )

2. ( c ) cos⁻¹ (\(\cfrac{\sqrt3}2\))

3. ( d ) tan⁻¹ (√3)

4. ( c ) \(\cfrac{\pi}2\) 

5. ( c ) [ −1, 1 ], [0 , π]