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Maths-

General

Easy

Question

Triangle ABC is similar to triangle DEF, where angle A corresponds to angle D. What is the value of $cos invisible function application F$ ?

The correct answer is: 0.8

HINT: Since triangles are similar, the sides are proportional and angles are the same.
Complete step by step Solution
Given that ΔABC is similar to ΔDEF.
∠A =∠D (given)
∠ACB =∠DFE (since they are similar)
From the figure, ∠ABC = ∠DEF = 90°.
Since these two triangles are similar, the sides are proportional.
That is, $fraction numerator A B over denominator D E end fraction equals fraction numerator B C over denominator E F end fraction equals fraction numerator C A over denominator F D end fraction$ .
$cos invisible function application F equals fraction numerator E F over denominator F D end fraction$
$cos invisible function application C equals fraction numerator B C over denominator A C end fraction equals 24 over 30 equals 4 over 5$
We have, $fraction numerator B C over denominator E F end fraction equals fraction numerator C A over denominator F D end fraction$
This can be written as $fraction numerator B C over denominator C A end fraction equals fraction numerator E F over denominator F D end fraction equals cos invisible function application F$
We got, $fraction numerator B C over denominator A C end fraction equals 4 over 5 equals fraction numerator E F over denominator F D end fraction equals cos invisible function application F$
Hence $cos invisible function application F equals 4 over 5$

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