Two men on either side of a temple of 30 meters high observe its top a

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. ( 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]