The diagonal of a TV is 30 inches long. Assuming that this diagonal forms a pair of 30-60-90 right triangles, what are the exact
length and width of the TV?
A: 15 inches by 15√3 inches
B: 60 inches by 60√3 inches
C: 15√2 inches by 15√2 inches
D: 60√2 inches by 60√2 inches
A: 15 inches by 15√3 inches
B: 60 inches by 60√3 inches
C: 15√2 inches by 15√2 inches
D: 60√2 inches by 60√2 inches
1 answer:
Your answer is A: 15 inches by 15√3 inches.
We can use trigonometry to solve this. If we draw out one of the triangles we can label the 30 inch side as the hypotenuse, and then the other sides as the opposite and adjacent. Then we just have to find the lengths of these.
To find the opposite, we use the trigonometric ratio sinθ = opposite ÷ hypotenuse, and thus the opposite is sin(60) × 30 = 15√3
Automatically now we know the answer is A because that is the only option with 15√3 as a side, but you could also solve using cosθ = adjacent ÷ hypotenuse and get the other side.
I hope this helps!
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Complete Question
Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89 z. Assume that the conditions for inference were met.calculate the p-value for Ellie's significance test
Answer:
The p-value is
Step-by-step explanation:
From the question we are told that
The percentage of senior citizens is p = 0.10
The sample size is
The sample proportion is
The test statistics is
The null hypothesis is
The alternative hypothesis is
Generally the p-value is mathematically represented as
From the z-table
=>
=>