(a) The triangle ABC has sides AB = 17m, BC = 12m and AC = 10m. Calculate the :
(i) largest angle of the triangle ; (ii) area of the triangle.
(b) From a point T on a horizontal ground, the angle of elevation of the top R of a tower RS, 38m high is 63°. Calculate, correct to the nearest metre, the distance between T and S.
Explanation
(a) (i)
(cos C = frac{a^{2} + b^{2} – c^{2}}{2ab})
(cos C = frac{12^{2} + 10^{2} – 17^{2}}{2(12)(10)})
(cos C = frac{-45}{240} = -0.1875)
(C = cos^{-1} (-0.1875))
= (100.81°)
(ii) Area of (Delta ABC = frac{1}{2} ab sin C)
= (frac{1}{2} times 12 times 10 times sin 100.81)
= (60 times 0.9822)
= (58.936 m^{2})
(b) (tan 63 = frac{38}{x})
(x = frac{38}{tan 63})
(x = 19.362 m)
(approxeq 19 m)