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Independant learners may find these practice non right angled trigonometry exercises useful.
1) For the following non right angled triangles, sketch and label them using standard notation and find all the sides and angles.
Use the sine rule for (a) and (b) and the cosine rule for (c) and (d)
(a) A = 37º, B = 73º, b = 4.30m
(b) A = 71º, B = 36º, a = 23.7mm
(c) y = 11cm (110mm), z =15cm (150mm), X = 55º
(d) x = 62.8mm, y = 41.2mm, Z = 62º
2) A lean-to conservatory has a base which is 7.5m long by 4m wide. The glazed roof makes an angle of 36º to the horizontal, across the 4m width. (right angle trigonometry)
Calculate;
(a) the length of the sloping roof in metres to 1 decimal place.
(b) the area of the glazed roof in m2 to 1 d.p.
Sine rule
a ÷ sin A = b ÷ sin B = c ÷ sin C
Cosine rule
a^2 = b^2 + c^2 – 2bc cos A
or
b^2 = a^2 + c^2 – 2ac cos B
or
c^2 = a^2 + b^2 – 2ab cos C
3) A vertical aerial mast RS is 21.8m high and stands on ground that is inclined 13º to the horizontal. A steel cable connects the top of the aerial R to a point T on the ground 8m downhill from S at the foot of the aerial mast. Using right-angle trig ratios, calculate the;
(a) length of the stay TR to the nearest 10mm
(b) angle that the cable makes with the horizontal ground in degrees, minutes and seconds (hint take length TS to be the hypotenuse of a right angled triangle for the first part of the calculation.)
4) The mast of a jib crane is 3m tall and the stay is 4.8m long.
The angle between mast and stay is 120º.
Find the length of the jib.
Acknowledgements to Topliss, Hurst & Skarratt
Model answers for these knowledge check self assessments can be down loaded (here) and are shown below...
Self Assessments Trigonometry.pdfPage updated
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