Question

11. A sailing boat with triangular masts is shown below. Two right triangles can be observed. Triangles ABC and ABD, both right-angled at B. The distance BC = 1 m and BD = 2 m and height AB = 4 m.
(A) The value of sec D is:
(a) 1 (b) √5 (c) √5 (d) 2 √52 √5
(B)The value of cosec C is:
(a) 4 (b) 1 (c)√17 (d)√17 √17 √17 4
(C)The value of tan D + cot C is:
(a)9 (b)9 (c)4 (d) 2 42 9 √17
(D) Value of sin2 C + cos2 D is:
(a) 0 (b) 1 (c) 97 (d) 85 85 97
(E) In ∆ ABC, Write tan A+B in terms of tan C.

Answer 1

Answer:

√5

Step-by-step explanation:

tan α = Perpendicular / Base  

tan D  = AB/BD  

⇒ tan D = 4/2  

⇒ tan D = 2  

Sec²D = 1 + tan²D  

⇒ Sec²D = 1 + 2²  

⇒ Sec²D = 1 + 4  

⇒ Sec²D = 5  

⇒ Sec D = √5  

∴ Value of sec D is: √5

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