In an isosceles triangle abc with base ac, the side ab is 14 and the cosine of A is √195: 14. Find the height to the base
| August 19, 2021 | education
The height BH, drawn to the base, forms a right-angled triangle ABH, in which we determine the sine of the angle BAN.
Sin2BAH + Cos2BAH = 1
Sin2BAH = 1 – Cos2BAH = 1 – (√195 / 14) 2 = 1 – 195/196 = (196 – 195) / 196.
SinBAH = 1/14.
Then SinBAH = BH / AB.
BH = AB * SinBAH = 14 * 1/14 = 1 cm.
Answer: The length of the BH height is 1 cm.
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