Question

In triangle ABC, tan(CAB) = and the 7 foot of the perpendicular from A to BC is D. If BD = 3, DC= 17, then find AD.​

Answer 1

Answer:

the given figure ab parallel DC and D A perpendicular AP if DC = angle abc = 10 B = 37cl perpendicular to the area of the tip of trapezium ABCD isthe given figure ab parallel DC and D A perpendicular AP if DC = angle abc = 10 B = 37cl perpendicular to the area of the tip of trapezium ABCD is

Answer 2

Given :- in triangle ABC, tan(angleCAB) = 22/7 and the foot of perpendicular from A to BC is D if BD = 3, DC = 17 .

To Find :- Length of AD = ?

Solution :-

Let us assume that, length of AD is x .

now, in right ∆ADB, we have,

→ tan (∠DAB) = DB/AD

→ tan (∠DAB) = (17/x) ------ Eqn.(1)

and, in right ∆ADC, we have,

→ tan (∠DAC) = DC/AD

→ tan (∠DAC) = (3/x) ------ Eqn.(1)

now,

→ ∠CAB = ∠DAB + ∠DAC

using tan both sides ,

→ tan (∠CAB) = tan (∠DAB + ∠DAC)

using in RHS :-

tan(A + B) = tan A + tan B / (1 - tan A * tan B)

putting values from Eqn.(1) and Eqn.(2) in RHS and given value in LHS now,

→ 22/7 = {(17/x) + (3/x)} / {1 - (17/x)(3/x)}

→ 22/7 = (20/x) / {1 - (51/x²)}

→ 22/7 = (20/x) * x²/(x² - 51)

→ 22/7 = 20x/(x² - 51)

→ 22(x² - 51) = 140x

→ 11x² - 70x - 561 = 0

→ 11x² - 121x + 51x - 561 = 0

→ 11x(x - 11) + 51(x - 11) = 0

→ (x - 11)(11x + 51) = 0

putting both equal to zero we get,

→ x = 11 and (-51/11)

since value of perpendicular height cant be in negative.

Hence, we can conclude that, length of AD(x) is equal to 11 cm .

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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