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Maths-

General

Easy

Question

In the right triangle above, sin $theta equals 2 over 5$ . If AC = $square root of n$ , what is the value of n?

The correct answer is: 84

Step by step explanation:
Given:
In $straight triangle ABC$ ,
$Sin invisible function application theta equals 2 over 5$
AB = 10,
AC = $square root of n$
Step 1:
We know that, in right angle triangle
sin $theta equals fraction numerator text Perpendicular end text over denominator text Hypotenus end text end fraction$
So, according to given information,
sin $theta equals BC over AB$
Step 2:
Put value of sin $theta equals 2 over 5$
$not stretchy rightwards double arrow 2 over 5 equals fraction numerator B C over denominator 10 end fraction$
Step 3:
Now, cross multiply each other
$not stretchy rightwards double arrow B C equals fraction numerator 10 cross times 2 over denominator 5 end fraction$
⇒ BC = 4
Step 2:
In $straight triangle ABC$ ,
Apply pythagorus theorem,
⇒ AC² + BC²= AB²
$not stretchy rightwards double arrow left parenthesis square root of n right parenthesis squared plus 4 squared equals 10 squared open curly brackets because left parenthesis square root of a right parenthesis squared equals a close curly brackets$
⇒ n + 16 = 100
⇒ n = 100 - 16
n = 84

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