Question

In the adjacent figure, angleB=90° and
DE || BC.If AD= sin teta, DB=cos teta
AE=1, then EC=​

Answer 1

Step-by-step explanation:

hey muatafa aapne figure hi di nahi so how can we give u answer

aapne angle theta konsa hai woh bhi nahi bataya

Answer 2

$EC=cot\theta$

Step-by-step explanation:

$\angle B=90^{\circ}$

$AD=sin\theta$

$DB=cos\theta$

AE=1

$DE\parallel BC$

$\angle ADE=\angle B=90^{\circ}$

Reason: corresponding angle theorem

$\angle AED=\angle ACB$

Reason: corresponding angle theorem

$\triangle$ADE$\sim \triangle$ABC

Reason: AA similarity postulate

When two triangle are similar then the ratio of their corresponding sides are equal

$\frac{AD}{AB}=\frac{DE}{BC}=\frac{AE}{AC}$

$\frac{sin\theta}{sin\theta+cos\theta}=\frac{1}{1+EC}$

$sin\theta+ECsin\theta=sin\theta+cos\theta$

$ECsin\theta=sin\theta+cos\theta-sin\theta=cos\theta$

$EC=\frac{cos\theta}{sin\theta}$

$EC=cot\theta$

$cot\theta=\frac{cos\theta}{sin\theta}$

#Learns more:

https://brainly.in/question/13446745