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Sagot :
Answer:
0.69
Step-by-step explanation:
In a right triangle, the cosine of one of the acute angles is the ratio of the adjacent ("next to") side to the hypotenuse.
In this triangle, the side adjacent to angle T has length [tex]\sqrt{38}[/tex]. Now you need the length of the hypotenuse, ST. Use the Pythagorean Theorem:
[tex]ST^2=(\sqrt{38})^2+(\sqrt{41})^2 \\\\ST^2=38+41\\\\ST=\sqrt{79}[/tex]
Build the ratio (adjacent) / (hypotenuse) and approximate it with a decimal.
[tex]\cos{T}=\frac{\sqrt{38}}{\sqrt{79}} \approx 0.69[/tex]
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To find :-
Cos T = ?
Given :-
Perpendicular(P) = RS = √41
Base(B) = RT = √38
Formula to be used :-
We will use here a trignometry formula to find hypotenuse (H) which is ST.
(hypotenuse)² = (perpendicular)² + (base)²
[tex] \cos(A) = \frac{base}{hypotenuse} [/tex]
Solution:-
H² = P² + B²
H² = (√41)² + (√38)²
H² = 41 + 38
H² = 79
H = √79
[tex] \cos(T) = \frac{B}{H} \\ \cos(T) = \frac{ \sqrt{38} }{ \sqrt{79} } \\ \cos(T) = \frac{6.17}{8.89} \\ \cos(T) = 0.69[/tex]
Result :-
The value of cos(T) is 0.69.
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