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Mathematics · Introduction to Trigonometry · NCERT Examples

Example 6

A complete, independently verified solution for NCERT Example 6.

Mathematics · Chapter 8 · NCERT Examples

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NCERT Example

Example 6

special angles · 30 degrees

In right triangle ABC, right-angled at B, AB = 5 cm and angle ACB = 30°. Find BC and AC.

Right triangle ABC, right-angled at B, with AB 5 centimetres and angle C equal to 30 degrees.
Figure 8-19 from the supplied NCERT chapter.

Solution

Board-exam working:

tan⁡30∘=ABBC\tan30^\circ=\frac{AB}{BC}
13=5BC\frac1{\sqrt3}=\frac5{BC}
BC=53 cmBC=5\sqrt3\text{ cm}
sin⁡30∘=ABAC\sin30^\circ=\frac{AB}{AC}
12=5AC\frac12=\frac5{AC}
AC=10 cmAC=10\text{ cm}

Final answer

BC = 5√3 cm and AC = 10 cm.