When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 35°31'.
If Joey is known to be standing 33 feet from the base of the tree, how tall is the tree (to the nearest foot)?
To find the height of the tree, we can use the tangent function.
Let's denote the height of the tree as h.
The tangent of the angle of depression is equal to the opposite side (height of the tree, h) divided by the adjacent side (distance between Joey and the base of the tree, 33 feet).
So, tan(35°31') = h/33.
Using a scientific calculator, we find that tan(35°31') ≈ 0.6929.
Now, we can find the height of the tree, h:
0.6929 = h/33.
Multiplying both sides of the equation by 33:
0.6929 * 33 = h.
Simplifying:
h ≈ 22.8827.
Rounding to the nearest foot, the height of the tree is approximately 23 feet.
Answers:
A)
26 ft
B)
24 ft
C)
30 ft
D)
28 ft
Based on the calculations, the height of the tree is approximately 23 feet.
None of the provided answer options (A, B, C, D) match this result.
Find the exact values of the indicated trigonometric functions.
Write fractions in lowest terms.
15 9 12
Find sin A and cos A.
To find the trigonometric functions sin A and cos A, we need additional information or a diagram that shows the relationship between the values 15, 9, and 12.
Without more information, we can't determine the exact values of sin A and cos A.
Find the median for the given frequency distribution.
two way table ( (Value Frequency)( 0 8)( 1 12)( 2 15)( 3 20)( 4 20)( 5 14) )
To find the median for the given frequency distribution, we need to first determine the cumulative frequency.
Using the given frequency distribution, we can calculate the cumulative frequency by adding up the frequencies as we go down the table:
(Value Frequency Cumulative Frequency)
0 8 8
1 12 8 + 12 = 20
2 15 20 + 15 = 35
3 20 35 + 20 = 55
4 20 55 + 20 = 75
5 14 75 + 14 = 89
The median is the middle value of the data set. Since we have a total of 89 values, the median will be the value in the 44th position (middle position if the total number of values is odd).
To determine the median, we find the value that corresponds to a cumulative frequency of 44, which is in the third class (2).
Therefore, the median for the given frequency distribution is 2.
Solve the problem.
What is the angle of elevation of the sun when a 70-ft flag pole casts a 24-ft shadow?
Round to the nearest tenth of a degree.
To find the angle of elevation of the sun, we can use the trigonometric function tangent. The tangent of an angle of elevation is given by the opposite side (height of the flagpole) divided by the adjacent side (length of the shadow).
Let h be the height of the flagpole.
Let s be the length of the shadow.
We are given that h = 70 ft and s = 24 ft.
Using the tangent function, we can write:
tan(angle of elevation) = h / s
Let's substitute the given values:
tan(angle of elevation) = 70 / 24
Using a scientific calculator, we find that tan(angle of elevation) ≈ 2.9167.
To find the angle of elevation, we take the inverse tangent (arctan) of both sides:
angle of elevation = arctan(2.9167)
Using a scientific calculator, we find that angle of elevation ≈ 70.04 degrees.
Rounding to the nearest tenth of a degree, the angle of elevation of the sun when the flagpole casts a 24-ft shadow is approximately 70.0 degrees.
Answers:
Question 12 options:
A)
69.9°
B)
71.1°
C)
18.9°
D)
20.1°