Question

Pls help me with this!

Answer 1

0.69

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
`√(38)`. Now you need the length of the hypotenuse, ST. Use the Pythagorean Theorem:

`ST^2=(√(38))^2+(√(41))^2 \\\\ST^2=38+41\\\\ST=√(79)`

Build the ratio (adjacent) / (hypotenuse) and approximate it with a decimal.

`cos(T)=(√(38))/(√(79)) \approx 0.69`

Answer 2

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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

`\cos(A) = (base)/(hypotenuse)`

Solution:-

H² = P² + B²

H² = (√41)² + (√38)²

H² = 41 + 38

H² = 79

H = √79

`\cos(T) = (B)/(H) \\ \cos(T) = ( √(38) )/( √(79) ) \\ \cos(T) = (6.17)/(8.89) \\ \cos(T) = 0.69`

Result :-

The value of cos(T) is 0.69.