Question 1 [3 marks]
Using the sine rule, x ÷ sin(38°) = 13 ÷ sin(100°), so x = 8.1 cm (1 d.p.).
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Using the sine rule, x ÷ sin(38°) = 13 ÷ sin(100°), so x = 8.1 cm (1 d.p.).
Using the sine rule, x ÷ sin(32°) = 15 ÷ sin(110°), so x = 8.5 cm (1 d.p.).
Using the sine rule, x ÷ sin(40°) = 12 ÷ sin(105°), so x = 8.0 cm (1 d.p.).
Using the sine rule, x ÷ sin(28°) = 14.5 ÷ sin(115°), so x = 7.5 cm (1 d.p.).
Using the sine rule, x ÷ sin(36°) = 11 ÷ sin(102°), so x = 6.6 cm (1 d.p.).
Using the sine rule, x ÷ sin(34°) = 16 ÷ sin(108°), so x = 9.4 cm (1 d.p.).
Using the sine rule, x ÷ sin(30°) = 13.5 ÷ sin(112°), so x = 7.3 cm (1 d.p.).
Using the sine rule, x ÷ sin(39°) = 12.5 ÷ sin(104°), so x = 8.1 cm (1 d.p.).
Using the sine rule, x ÷ sin(35°) = 14 ÷ sin(106°), so x = 8.4 cm (1 d.p.).
Using the sine rule, x ÷ sin(37°) = 15.5 ÷ sin(103°), so x = 9.6 cm (1 d.p.).
Using the sine rule, x ÷ sin(45.0°) = 6.7 ÷ sin(95°), so x = 4.76 cm (3 s.f.).
Using the sine rule, x ÷ sin(50.0°) = 7.2 ÷ sin(92°), so x = 5.52 cm (3 s.f.).
Using the sine rule, x ÷ sin(47.0°) = 6 ÷ sin(98°), so x = 4.43 cm (3 s.f.).
Using the sine rule, x ÷ sin(45.0°) = 7.5 ÷ sin(93°), so x = 5.31 cm (3 s.f.).
Using the sine rule, x ÷ sin(45.0°) = 6.4 ÷ sin(96°), so x = 4.55 cm (3 s.f.).
Using the sine rule, x ÷ sin(45.0°) = 7 ÷ sin(94°), so x = 4.96 cm (3 s.f.).
Using the sine rule, x ÷ sin(47.0°) = 6.8 ÷ sin(97°), so x = 5.01 cm (3 s.f.).
Using the sine rule, x ÷ sin(45.0°) = 7.3 ÷ sin(91°), so x = 5.16 cm (3 s.f.).
Using the sine rule, x ÷ sin(47.0°) = 6.5 ÷ sin(99°), so x = 4.81 cm (3 s.f.).
Using the sine rule, x ÷ sin(45.0°) = 7.1 ÷ sin(95°), so x = 5.04 cm (3 s.f.).
Shared vertical height h = √13² − 5² = 12.0 cm. Third angle in the left triangle = 180° − 40° − 65° = 75.0°. Sine rule: x ÷ sin(75.0°) = h ÷ sin(40°), so x = 18.0 cm (1 d.p.).
Shared vertical height h = √15² − 6² = 13.7 cm. Third angle in the left triangle = 180° − 38° − 62° = 80.0°. Sine rule: x ÷ sin(80.0°) = h ÷ sin(38°), so x = 22.0 cm (1 d.p.).
Shared vertical height h = √12² − 4.5² = 11.1 cm. Third angle in the left triangle = 180° − 42° − 68° = 70.0°. Sine rule: x ÷ sin(70.0°) = h ÷ sin(42°), so x = 15.6 cm (1 d.p.).
Shared vertical height h = √14.5² − 5.5² = 13.4 cm. Third angle in the left triangle = 180° − 39° − 64° = 77.0°. Sine rule: x ÷ sin(77.0°) = h ÷ sin(39°), so x = 20.8 cm (1 d.p.).
Shared vertical height h = √11.5² − 4² = 10.8 cm. Third angle in the left triangle = 180° − 44° − 66° = 70.0°. Sine rule: x ÷ sin(70.0°) = h ÷ sin(44°), so x = 14.6 cm (1 d.p.).
Shared vertical height h = √16² − 6.5² = 14.6 cm. Third angle in the left triangle = 180° − 36° − 60° = 84.0°. Sine rule: x ÷ sin(84.0°) = h ÷ sin(36°), so x = 24.7 cm (1 d.p.).
Shared vertical height h = √13.5² − 5.2² = 12.5 cm. Third angle in the left triangle = 180° − 41° − 67° = 72.0°. Sine rule: x ÷ sin(72.0°) = h ÷ sin(41°), so x = 18.1 cm (1 d.p.).
Shared vertical height h = √12.5² − 4.8² = 11.5 cm. Third angle in the left triangle = 180° − 43° − 63° = 74.0°. Sine rule: x ÷ sin(74.0°) = h ÷ sin(43°), so x = 16.3 cm (1 d.p.).
Shared vertical height h = √14² − 5.8² = 12.7 cm. Third angle in the left triangle = 180° − 37° − 65° = 78.0°. Sine rule: x ÷ sin(78.0°) = h ÷ sin(37°), so x = 20.7 cm (1 d.p.).
Shared vertical height h = √15.5² − 6.2² = 14.2 cm. Third angle in the left triangle = 180° − 40° − 61° = 79.0°. Sine rule: x ÷ sin(79.0°) = h ÷ sin(40°), so x = 21.7 cm (1 d.p.).