# trig

A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 24. From a point 1000 feet closer to the mountain along the plain, they find that the angle of elevation is 27.
How high (in feet) is the mountain?

1. 👍
2. 👎
3. 👁
1. Make a sideview sketch
you should have 2 triangles, one right-angled containing the height and a scalene triangle with angles 24° , 153° (the supplement of 27°) and 3°
the side opposite the 3° angle is 1000
by let the side opposite the 24° be x, (also the hypotenuse of the right-angled triangle)

x/sin24 = 1000/sin3
x = 1000sin24/sin3

let the height of the mountain be h
sin 27 = h/x
h = x sin27 = (1000sin24/sin3)(sin27)
= 3528.25

1. 👍
2. 👎
2. what....the......heck...is....trig..........

1. 👍
2. 👎
3. d = hor. distance from foot of mountain to point where 24 deg. is measured.
Tan24 = h/d, h = d*Tan24.
Tan27 = h/(d-1000), h = (d-1000)Tan27.

d*Tan24 = (d-1000)*Tan27,
d = (d-1000)*1.11,
0.9d = d-1000,
d = 10,000 Ft.
h = d*Tan24 = 4,450 Ft.

1. 👍
2. 👎
4. Howdy everyone, here's the equation you need for this:
tan 24 = h/((h/(tan 27)) + 1000)

Just plug your numbers into that equation and you'll have the right answer.

1. 👍
2. 👎

## Similar Questions

1. ### Precalculus

To estimate the height of a building, two students find the angle of elevation from a point (at ground level) down the street from the building to the top of the building is 33 degrees. From a point that is 300 feet closer to the

2. ### Physical Geography

Will someone please check my work? I cannot seem to post the map that is in the workbook. Assume that a parcel of air is forcd to rise up and over a 4000 meter high mountain.The initial temp of the parcel at sea level is 30*c, and

3. ### Algebra

A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then descends 200 ft to meet a fellow climber. Find the climber's elevation above sea level after meeting the other climber.

4. ### Physics

A projectile is fired with an initial velocity of 300m/s.upward at an angle of 30 degree with horizontal from a point 80m above the level plain. What horizontal distance will it cover before it strikes the plain?

1. ### statistics

A group of seven mountain climbers wishes to form a mountain climbing team of five.how many different teams could be formed?

2. ### Math

A back-to-back stem-and-leaf plot showing the points scored be each player on two different basketball teams is shown below. Team 1 | | Team 2 6 1| 0| 3 7 8 4 2| 1|4 6 8 9 9 6 3| 2|5 7 Key: 4|0|2 means 4 points for Team 1 2points

3. ### trig

You are skiing down a mountain with a vertical height of 1500 feet. The distance from the top of the mountain to the base is 3000 feet. What is the angle of elevation from the base to the top of the mountain?

4. ### PreCal

Angel of Elevation: You are skiing down a mountain with a vertical height of 1500 feet. The distance from the top of the mountain to the base is 3000 feet. What is the angle of elevation from the base to the top of the mountain?

1. ### trig

Bob is driving along a straight and level road straight toward a mountain. at some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 23 degrees 42 minutes. he then drives 1 mile

2. ### math

A mountain climber on Mt. Everest is at 29,035 feet above sea level. A stone at the bottom of the Dead Sea is at 1,349 ft below sea level. What pigsis the difference in elevation between the mountain climber and the stone?

3. ### math

A survey team is trying to estimate the height of a mountain above a level plain. From one point on the plain, they observe that the angle of elevation to the top of the mountain is 26 ∘ . From a point 2000 feet closer to the

4. ### Statistics

Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 4% at the 95% confidence level, how many randomly selected teenagers must we survey?