Theory question 109
Trigonometry(a) The triangle ABC has sides AB = 17 m, BC = 12 m and AC = 10 m. 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, 38 m high, is 63°. Calculate, correct to the nearest metre, the distance between T and S.
Show the model answer
Model answer
(a)(i) The largest angle is C, opposite AB. cos C = (122 + 102 − 172)/(2 × 12 × 10) = −45/240 = −0.1875, so C ≈ 100.8°.
(ii) Area = ½ × 12 × 10 × sin 100.8° ≈ 58.9 m2.
(b) tan 63° = 38/|TS|, so |TS| = 38/1.9626 ≈ 19.4 ≈ 19 m.
Explanation
The largest angle is opposite the longest side; a negative cosine means it is obtuse.