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The base of a triangle is 12 √3 cm and two angles at the base are 30° and 60° respectively. The altitude of the triangle is
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- 12 cm
- 6 cm
- 10 √3 cm
- 9 cm
Correct Option: D
2√3cm.
BD = x cm. (let)
∴ CD = (12√3 - x) cm.
∠ADB = ∠ADC = 90°
From ∆ ABD,
| tan 30° = | BD |
| ⇒ | = | √3 | BD |
| ⇒ AD = | ....(i) | √3 |
From ∆ ACD,
| tan 60 ° = | CD |
| ⇒ √3 = | 12√3 - x |
⇒ AD = √3 (12 √3 - x)
= 36 - √3 x ....(ii)
| ∴ x = | √3 |
⇒ x = 36 √3 * 3x
⇒ 4x = 36 √3
| ⇒ x = | = 9 √3 | 4 |
| ∴ AD = | = | = 9 cm. | √3 | √3 |
