Question

in the given figure, angle T and angle B are right angles. if the lengths of AT, ​

Answer 1

In the given figure, T and B are right angles. If the lengths of AT, BC and AS (in centimeters) are 15, 16 and 17 respectively, then the length of TC (in centimeters) is:



a)

18

b)

12

c)

19

d)

16

Correct answer is option 'C'. Can you explain this answer?

Related Test: Test: Problems On Similar Triangles

Answer 2

Answer:

C) 19cm

Step-by-step explanation:

In ∆ATS,

∠T= 90°

Therefore, By Pythagoras Theorem-

(17)^2 = (15)^2 + (TS) ^2

(TS) ^2 = (17)^2 - (15)^2

(TS) ^2 = 289 - 225

(TS)^2 = 64

(TS) = √64

Therefore, TS = 8cm

Now in ∆ATS and ∆ABC

∠BAC = ∠BAT (Common Angle)

∠ATS = ∠ABC (Both are equal to 90°)

Therefore, ∆ATS ~ ∆ABC (AA Similarity Criterion)

Now

BC/TS = AC/AS (Basic Proportionality Theorem)

16/8 = AT+CT/17

2 = 15+CT/17

15+CT = 34

CT = 34-15 = 19

Therefore CT = 19cm (Ans)