In the following figure, BD = 4cm DC=25cm. The line
AD is perpendicular to BC and AD=10cm. Find angle BAC.
Answers
∠BAC = 90° if BD = 4cm DC=25cm. The line AD ⊥ BC and AD=10cm
Step-by-step explanation:
AD ⊥ BC
=> AB ² = AD² + BD²
=> AB² = 10² + 4²
=> AB² = 116
=> AB = 2√29
=> AC ² = AD² +CD²
=> AC² = 10² + 25²
=> AC² = 725
=> AC = 5√29
BC = BD + DC = 4 + 25 = 29
BC² = 29² = 841
BC² = AB² + AC² - 2AB * AC Cos∠BAC
=> 841 = 116 + 725 - 2 * 2√29 * 5√29 Cos∠BAC
=> 0 = 580 Cos∠BAC
=> Cos∠BAC = 0
=> ∠BAC = 90°
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∠BAC is 90 degrees
Step-by-step explanation:
Consider the provided information.
BD = 4cm, DC=25cm. The line AD is perpendicular to BC and AD=10cm.
We need to find the angle BAC.
It is given that AD ⊥ BC
By using Pythagoras theorem:
AB ² = AD² + BD²
Substitute the respective.
AB² = 10² + 4²
AB² = 116
Also,
AC ² = AD² +CD²
AC² = 10² + 25²
AC² = 725
BC=BD+DC
BC=4+25=29
BC²=841
Now observe that if we add AB² and AC² we get BC² that means ΔABC must be right angle triangle where BC is the hypotenuse.
725+116=841
Hence, by converse of Pythagoras theorem ∠BAC is 90 degrees.
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