The feet of two vertical poles of heights 3metres and 7metres are in line with a point P on the ground, the smaller pole being between the taller pole and P at a distance 20metres from P. The angle of elevation of the top (T) of the taller pole from the top (R) of the smaller pole is 30◦. Calculate the: (i) distance RT (ii) distance of the foot of the taller pole from P, correct to 3s.fs. (iii) angle of elevation of T from P, correct to 1d.p. Please with full solution by a well recognized math teacher because I really don't want to fail it
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(i) Distance RT:
Using the Pythagorean Theorem, we can calculate the distance RT as follows:
RT = √(3^2 + 20^2) = 20.2 m
(ii) Distance of the foot of the taller pole from P:
Using the Law of Cosines, we can calculate the distance of the foot of the taller pole from P as follows:
Distance = √(7^2 + 20^2 - 2(7)(20)cos30°) = 24.3 m
(iii) Angle of elevation of T from P:
Using the Law of Sines, we can calculate the angle of elevation of T from P as follows:
Angle = sin-1(7/24.3) = 33.2°