Question

From the information given in the triangle 60 shown below, the length of CD is:

(take `sqrt3` = 1.732)

Options

• 7.32 m

• 27.32 m

• 10 m

• 17.32 m

Answer 1

7.32 m

Explanation:

In the larger right-angled triangle ABC with ∠B = 90°, height AB = 10 m, and base angle at C equal to 30°:

\[\text{BC} = \frac{\text{AB}}{\tan 30^\circ} = \frac{10}{\frac{1}{\sqrt{3}}} = 10\sqrt{3}\text{ m}\]

In the smaller right-angled triangle ABD with base angle at D equal to 45° and height AB = 10 m:

\[\text{BD} = \frac{\text{AB}}{\tan 45^\circ} = \frac{10}{1} = 10\text{ m}\]

The length of segmentCD is the difference between BC and BD:

\[\text{CD} = \text{BC} - \text{BD} = 10\sqrt{3} - 10 = 10(1.732) - 10 = 17.32 - 10 = 7.32\text{ m}\]