# Case study Chapter 2 (Inverse Trigonometry)

Case study 2:- Read the following and answer the question.(Case study inverse trigonometry 1)

Two men on either side of a temple 30 metres high observes 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 metres and the distance between the first person A and the temple is 30√3 metres.

(i) ∠CAB = α =

(a)      (b)

(c)                                    (d)

(ii) ∠CAB = α =

(a)                  (b)

(c)        (d)

(iii) ∠BCA = β =

(a)             (b)

(c)              (d)

(iv) ∠ABC =

(a) π/4                       (b) π/6

(c) π/2                         (d) π/3

(v) Domain and range of are respectively

(a) (-1, 1), (0, π)                (b) [-1, 1], (0, π)

(c) [-1, 1], [0, π]                 (d) (-1, 1), [-π/2, π/2]

Solution :We have

Now in ΔABD (right angled)

We have from (i)

In right ΔBCD, we have

ΔABC, we have,

∠ABC + ∠BAC  +  ∠ACB = 180°

⇒  ∠ABC + α + β = 180°

⇒  ∠ABC + 30 + 60 = 180

⇒  ∠ABC = 90

⇒  ∠ABC = π/2