The answer is D. They both had the same proportion.
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Answer:
343.7 ft
Step-by-step explanation:
The wire is anchored 190 -13 = 177 ft from the ground. That distance is opposite the given angle (31°). The measure you want is the hypotenuse of the triangle with that side and angle measures.
The mnemonic SOH CAH TOA reminds you that the relation between the opposite side, hypotenuse, and angle is ...
Sin(angle) = Opposite/Hypotenuse
Filling in the given information, you have ...
sin(31°) = (177 ft)/hypotenuse
Solving for hypotenuse gives
hypotenuse = (177 ft)/sin(31°) ≈ 343.7 ft
The length of the guy wire should be 343.7 ft.
Answer:
measure of ∠ABD = 42°
Step-by-step explanation:
Angle Formed by Tangent and Secant = (1/2)*(difference of Intercepted Arcs)
In this case the intercepted arcs are: minor arc AC and minor arc AD. Let´s first find minor arc AD, we know that:
minor arc AC + minor arc CD + minor arc AD = 360°
Then,
minor arc AD = 360° - minor arc AC - minor arc CD
minor arc AD = 360° - 72° - 132°
minor arc AD = 156°
Replacing in the aforementioned formula:
Angle Formed by Tangent and Secant = (1/2)*(difference of Intercepted Arcs)
∠ABD = (1/2)*(minor arc AD - minor arc AC)
∠ABD = (1/2)*(156° - 72°)
∠ABD = 42°
Answer:
2/45
Step-by-step explanation:
We are told that:
A jar contains 2 orange, 4 green, 2 white and 2 black balls.
The total number of balls in the jar is calculated as:
2 orange balls + 4 green balls + 2 white balls + 2 black balls = 10 balls
The probability of drawing an orange ball = P(Orange) = 2/10
The probability of drawing a black ball = P(Black) = 2/10
Therefore, the probability of drawing an orange ball without putting it back, then drawing a black ball is calculated as:
2/10 × 2/9 = 4/90
= 2/45
