The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.
1) Convert the angles to decimal form:
19' * 1°/60' = 0.32° => 21° 19' = 21.32°
20' * 1°/60' = 0.33° => 16° 20' = 16.33°
2) Deduce the trigonometric ratios from the verbal information.
You can form a triangle with
- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h
=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)
You can form a second triangle with:
- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h
=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)
Now equal the two expressions for h:
(x+65)*tan(16.33) = x*tan(21.32)
=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet
=> h = 195.73 * tan(21.32) = 76.39 feet.
Answer: 76.39 feet
Answer:
0 = 9x - 9x
0 = 0
This means it has infinite number of solutions.
Step-by-step explanation:
<h2>HOPE IT HELPS U!!!!</h2>
Please consider the attached image for complete question.
We have been given that measure of arc WY is 76° and and measure of arc XZ is 112°. We are asked to find the difference of of the measures of angle WPY and angle XPY.
First of all we will find the measure of angle WPY using intersecting secants theorem. Intersecting secants theorem states that measure of angle formed by two intersecting secants inside a circle is half the sum of intercepting arcs.
We can see that angle WPY and angle XPY are linear angles, so they will add up-to 180 degrees.
Now we need to find difference of both angles as:
Therefore, the difference of the measures of angle WPY and angle XPY is 8 degrees.
X = (12 +- sqrt (144 -4(7)(3))/14
x = (12 + - sqrt (144 - 84))/14
x = (12 + - sqrt(60))/14
x = (12 + - 2sqrt 15))/14
x = (6 + - sqrt 15) / 7
Answer:
525267262525226
Step-by-step explanation:
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