If Θ is between 0° and 90° and tanθ = 7/8 find cosθ

Since 0° < θ < 90°, you know that cos(θ) > 0.

Recall that

1 + tan²(θ) = sec²(θ)

and also that

sec(θ) = 1/cos(θ)

So if cos(θ) > 0, we also have 1/cos(θ) = sec(θ) > 0.

Then

sec(θ) = + √(1 + tan²(θ))

sec(θ) = √(1 + (7/8)²)

sec(θ) = √113 / 8

so that

cos(θ) = 1 / (√113 / 8) = 8 / √113

for finding the midpoint of any given 2 pair of points simply add the respective x coordinates with other x coordinate and the y coordinate with other y coordinate and divide them by 2

in your question it will be :

(3+1)/2 for the x coordinate of mid point i.e 2

[8+(-4)]/2 for the y coordinate of midpoint i.e 2

so coordinates of mid point of points (3,8) and (1,-4) will be (2,2)

answer is 12345678900987654321234567890987654321

step-by-step explanation: