In the given figure AD is perpendicular to BC- tan B - 34- tan C - 512 and BC - 56-Calculate the length of AD-

#160;Let BD = x cm and DC = y cm and AD = h cm #160;BC = BD + DC = x cm + y cm = 56 cm #160;tan B = h/x = 3/4 #160; #160;x/h = 4/3 ........ (1) #16 ...

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Standard IX

Mathematics

Basics of Geometry

In the given ...

Question

In the given figure $A D$ is perpendicular to $B C, tan B = \frac{3}{4}, tan C = \frac{5}{12}$ and $B C = 56$ .
Calculate the length of $A D$ .

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Solution

Let BD = x cm and DC = y cm and AD = h cm
BC = BD + DC = x cm + y cm = 56 cm
tan B = h/x = 3/4
x/h = 4/3 ........ (1)
tan C = h/y = 5/12
y/h = 12/5 ...... (2)
Adding (1) and (2) we get
(x + y)/h = (4/3) + (12/5) = (20 + 36)/15 = 56/15
=> 56/h = 56/15
=> h = 15
=> AD= h cm = 15 cm

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In the given figure AD is perpendicular to BC,tanB=34,tanC=512 and BC=56.Calculate the length of AD.

Let BD = x cm and DC = y cm and AD = h cm BC = BD + DC = x cm + y cm = 56 cm tan B = h/x = 3/4 x/h = 4/3 ........ (1) tan C = h/y = 5/12 y/h = 12/5 ...... (2) Adding (1) and (2) we get (x + y)/h = (4/3) + (12/5) = (20 + 36)/15 = 56/15 => 56/h = 56/15 => h = 15 => AD= h cm = 15 cm

In the given figure $A D$ is perpendicular to $B C, tan B = \frac{3}{4}, tan C = \frac{5}{12}$ and $B C = 56$ .
Calculate the length of $A D$ .

Let BD = x cm and DC = y cm and AD = h cm
BC = BD + DC = x cm + y cm = 56 cm
tan B = h/x = 3/4
x/h = 4/3 ........ (1)
tan C = h/y = 5/12
y/h = 12/5 ...... (2)
Adding (1) and (2) we get
(x + y)/h = (4/3) + (12/5) = (20 + 36)/15 = 56/15
=> 56/h = 56/15
=> h = 15
=> AD= h cm = 15 cm