Question

(a) if tan∅ = 8/15, find the value of

sin∅ + cos∅(1- cos∅) (b)The angle of elevation of the top of a radio mask from a point due east of it and 96m away from its base is 30degrees. From another point, due west of the mask, the angle of elevation of the top is 60degrees. Calculate the distance of the second point from the base of the mast.

Answer 1

Below in bold.

Explanation:

The right triangle of which ∅ is a part has

Hypotenuse = sqrt(8^2 + 15^2)

= sqrt289

= 17,

So, sin ∅ = 8/17 and cos ∅ = 15/17

and

sin∅ + cos∅(1- cos∅)

= 8/17 + 15/17(1 - 15/17)

= 8/17 + 15/17 - 225/289

= 166/289.

(b) tan 30 = h/96 where h is height of the mast

h = 96 tan 30.

= 55.4256

tan 60 = 55.4256/d where d is the required distance

d = 55.4256/ tAN60

= 32 M