In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=65°, and ZX = 4.8 feet. Find the length of YZ to the nearest tenth of a foot.

10.3

Step-by-step explanation:

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\tan X = \frac{\text{opposite}}{\text{adjacent}}=\frac{x}{4.8}

tanX=  

adjacent

opposite

=  

4.8

x

\tan 65=\frac{x}{4.8}

tan65=  

4.8

x

4.8\tan 65=x

4.8tan65=x

Cross multiply.

x=10.2936\approx \mathbf{10.3}\text{ feet}

x=10.2936≈10.3 feet

Type into calculator and round to the nearest tenth of a foot.

X

Y

Z

4.8

10.3

(adjacent to ∠X)

(opp. of ∠X)

(hypotenuse)

65°

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this

this is a good question! i’ll do some research and what i find, i’ll contact you asap when i have something! ✊