...inscribed between this circle and the sides containing the angle A . Ax2 2A L — sin-s- ) sec jr6. The sides of a triangle are proportional to the sines of the opposite angles. If the sides of a triangle are x' + x + l, Zx + 1, and i* — 1, find the greatest angle. 7. Show how...

...are of little value, and we shall therefore confine ourselves here to the first two cases. ,• 91. The sides of a triangle are proportional to the sines of the opposite angles. Let ABC be a triangle, and in each of the figures let the angle В be acute, while the angle С is...

...and j3 with it, and through D draw parallels to complete the parallelogram ABDC as in Art. 12. Since the sides of a triangle are proportional to the sines of the opposite angles, we have AB BD AD sinADB Km' BAD sinABD' AB BD AD ie, sin/3 sin a sin(a + /3)° ... =--A, =. sin (a...

...tables, taking A = 37° 46'. 9. Prove that cos(A— B) = cos A cos B + sin A sin B. 10. Prove that the sides of a triangle are proportional to the sines of the opposite angles. The angle of elevation of a tower at a certain place is 17°. On walking 60 yards nearnr to the tower...

...and j9 with it, and through D draw parallels to complete the parallelogram ABDC as in Art. 12. Since the sides of a triangle are proportional to the sines of the opposite angles, we have AB BD AD sin ADB sin BAD sin ABD ' ie AIL^HP-- AD -' sin. ft ~ sin o ~ sin (a + /3) " !=AD-^^-@—...

...will be often referred to as sides only. 8.2 THEOREM 1 In any triangle ABC Ь sin A sinß sin С [ie, the sides of a triangle are proportional to the sines of the opposite angles.] Proof: The triangle ABC may be an acute angled triangle [Fig. 8.1 (i)], obtuse angled [Fig. 8.1 (ii)]...

...(2) cos* A + cos4.S + cos4 С + вт4Л + sinlS •f sinV - 2 + cos 2 A cos 2S cos 2C. 4. Prove that the sides of a triangle are proportional to the sines of the 10 opposite angles. Three stations A, S, С on a horizontal plane are in a straight line passing through...