Find the missing value to the nearest hundredth.
tan =38
88.49m
61.25m
65.25m
44.25m
Find the missing value to the nearest hundredth.
sin=8/32
75.52m
14.04m
77.76m
14.48
Both Steve and I have answered this same question for you in two different posts.
Do you not read replies to your post?
To find the missing value, we need to use the properties of trigonometric functions.
First, let's find the missing value in the first question:
The given information is that tan = 38. We know that tangent (tan) is equal to the ratio of the opposite side to the adjacent side in a right triangle.
So, tan = opposite/adjacent
To find the missing value, we need to use the inverse tangent function (arctan) to get the angle in degrees.
arctan(38) = 86.41 degrees (rounded to the nearest hundredth)
Since we need to find the missing value, we can use the tangent function again:
tan(angle) = opposite/adjacent
tan(86.41) = opposite/88.49
We solve for the opposite:
opposite = tan(86.41) * 88.49
opposite = 88.49 * tan(86.41)
opposite ≈ 88.49 * 43.246
opposite ≈ 3826.32
So, the missing value to the nearest hundredth is 3826.32m.
Now, let's move on to the second question:
The given information is that sin = 8/32. We know that sine (sin) is equal to the ratio of the opposite side to the hypotenuse in a right triangle.
So, sin = opposite/hypotenuse
To find the missing value, we need to find the opposite side, which is the numerator of the given sin ratio.
opposite = 8
Now, let's find the hypotenuse. We can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the lengths of the two legs, and c is the length of the hypotenuse.
In this case, we have:
a = opposite = 8
b = unknown side
c = hypotenuse
Using the Pythagorean theorem:
8^2 + b^2 = c^2
64 + b^2 = c^2
Now, we substitute the values into the sin ratio:
sin = opposite/hypotenuse
8/c = 8/32
Now, we can solve for c (hypotenuse):
8/c = 8/32
Cross-multiplying, we get:
8 * 32 = 8 * c
256 = 8c
Now, divide both sides by 8:
c = 256/8
c = 32
So, the hypotenuse is 32.
Therefore, the missing value to the nearest hundredth is 32m.
To summarize:
First question: The missing value is approximately 3826.32m.
Second question: The missing value is exactly 32m.