While visiting yosemite national forrest, joe approximated the angle of elevation to the top of a hill to be 25 degrees. after walking 350 ft closer, he guessed that the angle of elevation had increased by 14 degrees. approximately how tall is the hill?

384.780390296928 feet

This value is approximate. Round it however you need to.

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Work Shown:

Refer to the attached image

Point A = initial observation point
Point B = new observation point
Point C = bottom of the hill (directly underneath point D)
Point D = top of the hill (directly overhead point C)

Segment lengths
AB = 350
BC = x
CD = y
AC = AB+BC = 350+x

The goal is to find the value of y.

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tan(angle) = opposite/adjacent
tan(25) = CD/AB
tan(25) = y/(350+x)
(350+x)*tan(25) = y
y = (350+x)*tan(25)
y = (350+x)*0.466307658155
y = 350*0.466307658155+x*0.466307658155
y = 163.20768035425+0.466307658155x
y = 0.466307658155x+163.20768035425

tan(angle) = opposite/adjacent
tan(39) = CD/BC
tan(39) = y/x
tan(39) = (0.466307658155x+163.20768035425)/x
x*tan(39) = 0.466307658155x+163.20768035425
x*0.809784033195 = 0.466307658155x+163.20768035425
0.809784033195x-0.466307658155x = 163.20768035425
0.34347637504x = 163.20768035425
0.34347637504x/0.34347637504 = 163.20768035425/0.34347637504
x = 475.164209868127

Now use this x value to find y
y = 0.466307658155x+163.20768035425
y = 0.466307658155*475.164209868127+163.20768035425
y = 384.780390296928

Therefore, the hill is approximately 384.780390296928 feet tall.

0.69 yards

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)