In ΔFGH, the measure of ∠H=90°, the measure of ∠G=85°, and GH = 4.5 feet. Find the length of FG to the nearest tenth of a foot.

51.6 feet

Step-by-step explanation:

\cos G = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{4.5}{x}

cosG=

hypotenuse

adjacent

​

=

x

4.5

​

\cos 85=\frac{4.5}{x}

cos85=

x

4.5

​

x\cos 85=4.5

xcos85=4.5

Cross multiply.

\frac{x\cos 85}{\cos 85}=\frac{4.5}{\cos 85}

cos85

xcos85

​

=

cos85

4.5

​

Divide each side by cos 85.

x=\frac{4.5}{\cos 85}=51.6317\approx 51.6\text{ feet}

x=

cos85

4.5

​

=51.6317≈51.6 feet

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.