Abc is a triangle where ab = 4, the median ad = 1, then find the minimum value of the angle bac?
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Given the median AD then :
BD = DC
The median cuts BC at 90°
Triangle ABD is a right angled triangle.
AB = 4
AD = 1
Using Pythagoras theorem to get BD:
4² - 1 = 15
√15 = 3.87 cm
Since BD = DC
We use trigonometric ratios to get angle BAD
Cos Ф = 1/4 = 0.25
Cos ⁻¹ 0.25 = 75.5°
Angle DAC:
Tan Ф = 3.87 / 1
Tan ⁻¹ 3.87 = 75.5 °
Angle BAC = DAC + BAD
= 75.52 +75.51 = 151.03°
BD = DC
The median cuts BC at 90°
Triangle ABD is a right angled triangle.
AB = 4
AD = 1
Using Pythagoras theorem to get BD:
4² - 1 = 15
√15 = 3.87 cm
Since BD = DC
We use trigonometric ratios to get angle BAD
Cos Ф = 1/4 = 0.25
Cos ⁻¹ 0.25 = 75.5°
Angle DAC:
Tan Ф = 3.87 / 1
Tan ⁻¹ 3.87 = 75.5 °
Angle BAC = DAC + BAD
= 75.52 +75.51 = 151.03°
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