The diagram shows a triangle `ABC` where `AC` = 25 cm, `BC` = 16 cm, `angle BAC` = 28° and angle `ABC` is obtuse.
Find the size of the obtuse angle `ABC` correct to the nearest degree. (3 marks)
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Trigonometry, 2ADV T1 EQ-Bank 2
Determine all possible dimensions for triangle `ABC` given `AB = 6.2\ text(cm)`, `angleABC = 35°` and `AC = 4.1`.
Give all dimensions correct to one decimal place. (3 marks)
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Show Worked Solution
`text(Using the sine rule:)`
| `(sinangleACB)/6.2` | `= (sin35^@)/4.1` |
| `sinangleACB` | `= (6.2 xx sin35^@)/4.1` |
| `= 0.8673…` | |
| `angleACB` | `= 60.15…^@\ text(or)\ 119.84…^@` |
`text(If)\ \ angleACB = 60.15^@,`
`angleBAC = 180 – (35 + 60.15) = 84.85^@`
| `(BC)/(sin84.85)` | `= 4.1/(sin35^@)` |
| `BC` | `= 7.11…` |
| `= 7.1\ text(cm)` |
`text(If)\ \ angleACB = 119.85^@,`
`angleBAC = 180 – (35 + 119.85) = 25.15^@`
| `(BC)/(sin25.15)` | `= 4.1/(sin35^@)` |
| `BC` | `= 3.03…` |
| `= 3.0\ text(cm)` |
`:.\ text(Possible dimensions are:)`
`text(7.1 cm, 6.2 cm, 4.1 cm or)`
`text(3.0 cm, 6.2 cm, 4.1 cm.)`
Trigonometry, 2ADV T1 2009 HSC 5c
The diagram shows a circle with centre `O` and radius 2 centimetres. The points `A` and `B` lie on the circumference of the circle and `/_AOB = theta`.
- There are two possible values of `theta` for which the area of `Delta AOB` is `sqrt 3` square centimetres. One value is `pi/3`.
Find the other value. (2 marks)
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- Suppose that `theta = pi/3`.
(1) Find the area of sector `AOB` (1 mark)
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(2) Find the exact length of the perimeter of the minor segment bounded by the chord `AB` and the arc `AB`. (2 marks)
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